(C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year is correct option.
Both Investment A and Investment B are annuities, but we need to determine which one is an ordinary annuity. An ordinary annuity is one in which payments are made at the end of each period, while in an annuity due, payments are made at the beginning of each period.
Looking at the table, we can see that Investment A and Investment B both have payments made at the end of each month, so they are both examples of ordinary annuities.
To calculate the future value of each annuity after one year, we can use the formula:
[tex]FV = P \times [(1 + r)^n - 1] / r[/tex]
where:
FV is the future value of the annuity
P is the payment amount
r is the interest rate per period (in this case, 3.5% per month)
n is the number of periods (12 in this case, since we're looking at one year)
For Investment A, we have P = 350, r = 0.035, and n = 12. Plugging these values into the formula, we get:
FV = 350 × [(1 + 0.035[tex])^12[/tex] - 1] / 0.035
= 3,906.64
Therefore, the answer is (C) Investment A is an ordinary annuity with 3,906.64 in the account after 1 year.
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Carlos built a rectangular fort that was 6 feet long and 4.5 feet wide. He determined that the area of his fort was 13.5 feet².
For your response, answer three questions.
1. What is the area of the fort?
2. Was Carlos correct? (yes or no)
3. If Carlos was not correct, what was his mistake? If Carlos was correct, how did he determine the area?
1. The area of the fort is 27 square feet.
2. No, Carlos was not correct
3. The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.
1. The area of the fort can be calculated by multiplying the length and width of the rectangle. In this case, the length is 6 feet and the width is 4.5 feet. Therefore, the area can be calculated as:
Area = Length × Width
= 6 feet × 4.5 feet
= 27 square feet
So, the area of the fort is 27 square feet.
2. No, Carlos was not correct. The actual area of the fort is 27 square feet, not 13.5 square feet as he determined.
3. Carlos made a mistake in his calculation. Instead of multiplying the length and width together, he likely mistakenly multiplied them as if he was finding the perimeter or added them together. The correct way to determine the area is to multiply the length and width, not add them. Carlos' mistake was in incorrectly calculating the area of the fort.
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Will Give Brainliest Please Help!
Answer:
The answer to this question is vertical angles
Step-by-step explanation:
angle 5 and 8
Those are vertical angles formed by two crossing lines and they are equal
12. Directors of a company claim that 90% of the workforce supports a new shift pattern that they have suggested. A random survey of 100 people in the workforce finds 85 in favour of the new scheme. Test if there is a significant difference between the survey results and the director's claim. What kind of test will you perform? Why? (2) 12.1 12.2 State the Alternative Hypothesis (2) 12.3 At what level of significance will you test the difference between the director's claim and the survey results? (2) 12.4 What kind of test in terms of the tails will you perform? (2) 12.5 Which value(s) indicate(s) the rejection region? (2) 12.6 Identify the numbers in the question and use them to calculate the test statistic. (5) 12.7 Referring to the rejection region and the test statistic, what will happen to the null hypothesis? (2) 12.8 Write your conclusion of the test. Remember to refer to the actual example.(2)
12.1 Alternative Hypothesis, 12.2 The level of significance will typically be set at α = 0.05 (5%), 12.3 In terms of tails, we will perform a two-tailed test. 12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test,
Answers to the aforementioned questionsTo test if there is a significant difference between the survey results and the director's claim, we will perform a hypothesis test using a one-sample proportion test.
12.1 Alternative Hypothesis: The alternative hypothesis would be that the proportion of the workforce supporting the new shift pattern is not equal to 90%. We can express this as H1: p ≠ 0.9.
12.2 The level of significance for testing the difference between the director's claim and the survey results will typically be set at α = 0.05 (5%).
12.3 In terms of tails, we will perform a two-tailed test. This is because we are testing if the proportion is significantly different from the claimed value (90%), which could be either higher or lower.
12.4 The rejection region is determined by the critical values corresponding to the significance level α. In a two-tailed test, we divide α equally between the two tails. So, the rejection region will be split into two parts, one in the left tail and one in the right tail.
12.5 The rejection region is determined by the critical values. In this case, the critical values will be based on the standard normal distribution and the significance level α. The values that indicate the rejection region are the critical values of the standard normal distribution associated with α/2 (in each tail) based on the sample size.
12.6 Let's calculate the test statistic. The sample proportion in favor of the new shift pattern is 85/100 = 0.85. The expected proportion under the null hypothesis is 0.9. The standard error can be calculated using the formula: SE = sqrt(p * (1-p) / n), where p is the expected proportion and n is the sample size. Plugging in the values, we have SE = sqrt(0.9 * 0.1 / 100) ≈ 0.03. The test statistic can be calculated as (sample proportion - expected proportion) / SE, which gives (0.85 - 0.9) / 0.03 ≈ -1.67.
12.7 Referring to the rejection region and the test statistic, if the test statistic falls within the rejection region (i.e., if it is beyond the critical values), we will reject the null hypothesis. If the test statistic is not in the rejection region, we will fail to reject the null hypothesis.
12.8 Based on the calculated test statistic of -1.67 and the critical values associated with α/2, we would compare the test statistic with the critical values to determine if it falls within the rejection region. If it does, we would reject the null hypothesis and conclude that there is a significant difference between the survey results and the director's claim.
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Question
Evaluate |—15u| + |3v| + 3 when u
=
3 and v = 3.
The value of given expression is 57.
We are given that;
|—15u| + |3v| + 3
u=3, v = 3
Now,
To evaluate the expression, you need to substitute the values of u and v and simplify. The absolute value of a number is the distance from zero on the number line, so it is always positive or zero. You can write your solution as:
|—15u| + |3v| + 3 = |—15(3)| + |3(3)| + 3 = |—45| + |9| + 3 = 45 + 9 + 3 = 57
Therefore, by the given expression the answer will be 57.
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n a recent trip to the convenience store, you picked up 3 gallons of milk, 5 bottles of water, and 8 snack-size bags of chips. Your total bill (before tax) was $28.50. If a bottle of water costs twice as much as a bag of chips, and a gallon of milk costs $1.90 more than a bottle of water, how much does each item cost?
A bag of chips costs $0.95, a bottle of Water Costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.
Let x be the cost of a bag of chips in dollars.
Since a bottle of water costs twice as much as a bag of chips, a bottle of water costs 2x dollars.
A gallon of milk costs $1.90 more than a bottle of water, so a gallon of milk costs 2x + $1.90 dollars.
Using the given information, we can set up the following equation to represent the total cost:
3(2x + $1.90) + 5(2x) + 8x = $28.50
Simplifying the equation, we get:
6x + $5.70 + 10x + 8x = $28.50
24x + $5.70 = $28.50
Subtracting $5.70 from both sides, we get:
24x = $22.80
Dividing both sides by 24, we get:
x = $0.95
Therefore, a bag of chips costs $0.95, a bottle of water costs 2*$0.95 = $1.90, and a gallon of milk costs 2*$0.95 + $1.90 = $3.80.
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Please I need answer of this question help me I have exam tomorrow men
Please upload an image or give a question.
A father is twice as old as his son,
what is the sum of their ages if the son’s age is X?
The sum of their ages if the son’s age is X is 3X.
We are given that;
x=A father is twice as old as his son
Now,
If the son’s age is X,
Then the father’s age = 2X.
The sum of their ages
= X + 2X
= 3X.
Therefore, by algebra the answer will be 3X.
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Help me find the following measure for this figure
Answer:
A = 36π units²
Step-by-step explanation:
the area (A) of a circle is calculated as
A = πr² ( r is the radius )
here r = 6 , then
A = π × 6² = 36π units²
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of center for the data, and what is its value?
The mean is the best measure of center, and it equals 19.
The median is the best measure of center, and it equals 4.
The median is the best measure of center, and it equals 19.
The mean is the best measure of center, and it equals 4.
The correct answer is: The median is the best measure of center, and it equals 19.
A box plot, also known as a box-and-whisker plot, is a graph that displays the distribution of a dataset.
The box represents the middle 50% of the data, with the bottom of the box being the first quartile (Q1) and the top of the box being the third quartile (Q3). The line inside the box represents the median.
The "whiskers" extend from the box to the dataset's minimum and maximum values or, in the case of outliers, a specific distance from the box (often 1.5 times the interquartile range).
The box plot in this instance reveals that the median number of tickets sold was 19, with the middle 50% of the data falling between 17 and 21 tickets sold.
A minimum of 10 and a maximum of 27 tickets may be sold before the whiskers are removed.
The median is the most suitable measure of the center for this dataset since it is the measure of the center that represents the middle of the dataset.
In light of this, the answer is "The median is the best measure of center, and it equals 19."
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Which value can be substituted for f to make the equation 2f - 3 = 9 true? A: f=3 B: f=6 C: f=4 D: f=7
m/3 = 82°. Find m/4.
m/4= ?
Answer: 98 deg
Step-by-step explanation:
angles 3 and 4 are supplementary; this means their sum is 180 degrees.
so simply put, 180 - angle 3 = angle 4
180 - 82 = 98
You purchase a couch for $509.84 plus 4% sales tax. The furniture store offers an installment loan that allows you to pay for the couch by making 12 equal monthly payments of $49.60. What is the cost of credit, in dollars, for this loan? Round your answer to the nearest cent.
Suppose the credit card company changes the program so Keenan earns 1 mile for every $8 he spends. How would that change the amount of money Keenan needs to spend to earn the miles for his trip?
Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.
If Keenan earns 1 mile for every $8 he spends, then he would need to spend 8 times as much money to earn the same number of miles as he did before.
In other words, he would need to spend $8 to earn 1 mile instead of $1 to earn 1 mile under the old program.
To calculate the new amount of money Keenan needs to spend to earn the miles for his trip, we would need to multiply the old amount by 8.
For example, if under the old program, Keenan needed to spend $10,000 to earn 25,000 miles for his trip, under the new program he would need to spend:
$10,000 x 8 = $80,000
So under the new program, Keenan would need to spend $80,000 to earn the 25,000 miles for his trip.
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5. Jada is comparing 2 functions.
a(x) = 2(2)*
b(x) = 4x² + 2x
She finds that a(2) = 8 and a(3) = 16, b(2) = 20 and b(3) = 42. She draws the conclusion
that the larger the x value, a will continue to greater than b as she saw in her 2
examples. Show or explain why Jada is not correct.
After considering the given data we conclude that Jada's conclusion is not correct because she only tested two values of x for each function and concluded that a will always be greater than b for larger x values.
So , this is not true in general. In order to see why, let's provide a specified comparison between the two functions for a general value of x by forming an algebraic expression
a(x) = 2(2) = 4
b(x) = 4x² + 2x
We clearly see that b(x) grows much faster than a(x) as x gets larger. In fact, for any value of x greater than 1/2, b(x) will be greater than a(x).
Then, Jada's conclusion is not correct in general.
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At the hot dog stand, it costs $18.39 for five hot dogs and six bags of chips. If it costs $4.63 for one hot dog and two bags of chips, how much is a hot dog?
A hot dog costs 2.25 we get it by solving the equation
Let's denote the cost of one hot dog by x.
Then we can set up two equations:
5x + 6y = 18.39
x + 2y = 4.63
where y is the cost of one bag of chips.
We want to solve for x.
Let us isolate variable y in the second equation
y = 4.63 - x/2
Substitute the y equation in the equation (1)
[tex]$5x + 6\left(\frac{4.63 - x}{2}\right) = 18.39$[/tex]
Simplifying this equation gives:
5x + 13.89 - 3x = 18.39
2x = 4.5
x = 2.25
Hence, a hot dog costs 2.25.
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find the derivative of f(x)=(3x^2−4x+1)^4
The derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)
The given function is f(x)=(3x²−4x+1)⁴
We have to find the derivative of the function
By using chain rule we find the derivative
f'(x)=4(3x²−4x+1)³ d/dx(3x²−4x+1)
=4(3x²−4x+1)³ (6x-4)
Hence, the derivative of the function is f'(x)=4(3x²−4x+1)³ (6x-4)
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A box contains 12 transistors, 5 of which are defective. If 5 are selected at random, find the probability of the statements below.
a. All are defective
b. None are defective
Answer:
a. The probability that all 5 selected transistors are defective is 0.0024 or 0.24%.
To calculate this probability, we use the formula for the probability of the intersection of independent events:
P(all 5 defective) = P(defective) x P(defective) x P(defective) x P(defective) x P(defective)
where P(defective) = 5/12 for each transistor.
Plugging in the values, we get:
P(all 5 defective) = (5/12) x (5/12) x (5/12) x (5/12) x (5/12) = 0.0024
b. The probability that none of the selected transistors are defective is 0.163 or 16.3%.
To calculate this probability, we use the complement rule:
P(none defective) = 1 - P(at least one defective)
To calculate P(at least one defective), we can use the complement rule again:
P(at least one defective) = 1 - P(none defective)
So, we need to find P(none defective) first:
P(none defective) = P(not defective) x P(not defective) x P(not defective) x P(not defective) x P(not defective)
where P(not defective) = 7/12 for each transistor.
Plugging in the values, we get:
P(none defective) = (7/12) x (7/12) x (7/12) x (7/12) x (7/12) = 0.163
Then, we can find P(at least one defective):
P(at least one defective) = 1 - P(none defective) = 1 - 0.163 = 0.837
Finally, we can find P(none are defective) using the complement rule:
P(none defective) = 1 - P(at least one defective) = 1 - 0.837 = 0.163.
Solve for x. Assume that lines which appear tangent are tangent.
The value of x using Tangent - Secant theorem is: 16
How to solve the Tangent-secant Theorem?The tangent-secant theorem states that when a tangent and secant possess a common endpoint outside the circle the product of the secant and the external part of the secant is equal to the square of the tangent.
We are given:
internal part of the secant = (x + 9),
external part of the secant = 9,
tangent = 15,
According to Tangent-secant Theorem:
(x + 9) * 9 = 15²
9x + 81 = 225
9x = 144
x = 144/9
x = 16
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un auto parte de reposo y se desplaza con una aceleración de 1m/s2 durante 1s. luego se apaga el motor y el auto desacelera debido al rozamiento durante 10s a un promedio de5 cm/s2. entonces se le aplica los frenos y se detiene 5s despues ¿ calcular la distancia total recorrida?
After considering all the given data we conclude that the total distance traveled by the car is 285m, under the condition that the given car starts from rest and moves with an acceleration of 1m/s2 for 15.
The distance traveled during this time can be evaluated using the formula
[tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (0),
a = acceleration (1m/s2)
t = time (15s).
Placing in these values we get
s = 0 + (1/2) × 1 × 15²
= 112.5m .
After this, the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. The distance traveled during this time can be evaluated applying the formula
[tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (the final velocity of the previous step),
a = acceleration (-0.05m/s2)
t = time (10s).
Placing in these values we get
s = 112.5 + (1/2) × (-0.05) × 10²
= 87.5m.
Finally, brakes are applied and it stops after 5s. The distance traveled during this time can be evaluated using the formula [tex]s = ut + (1/2)at^2[/tex]
Here,
s = distance traveled,
u = initial velocity (the final velocity of the previous step),
a = acceleration (-0.05m/s2)
t = time (5s).
Placing in these values we get s = 87.5 + (-0.05)× 5² = 85m.
Therefore, total distance traveled by car can be calculated by adding all three distances together which gives us
112.5m + 87.5 + 85
= 285m.
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The complete question is
A car starts from rest and moves with an acceleration of 1m/s2 for 15. Then the engine is turned off and the car decelerates due to friction for 10s at an average of 5 cm/s2. then the brakes are applied and it stops 5s after calculating the total distance traveled?
Tuy lồ,
18,
A radioactive compound with mass 480 grams decays at a rate of 15.1% per hour.
Which equation represents how many grams of the compound will remain after 2
hours?
OC=480(1-0.151)
OC=480(1-0.151) (1 - 0.151)
OC=480(1+0.151)²
OC=480(0.151)²
(1 -0.151) (1 - 0.151)
Match each absolute value inequality on the left side with its solution set on the right
The inequality 2|x - 3| + 6 > 10 has the solution set:
x < 1 or x > 5
To solve the inequality 2|x - 3| + 6 > 10, we need to isolate the absolute value expression |x - 3|.
We can do this by subtracting 6 from both sides of the inequality:
2|x - 3| > 4
Then we can divide both sides by 2:
|x - 3| > 2
Now we need to consider two cases, one where x - 3 is positive, and another where it is negative:
When x - 3 is positive, the inequality |x - 3| > 2 becomes:
x - 3 > 2
Solving for x gives:
x > 5
When x - 3 is negative, the inequality |x - 3| > 2 becomes:
-(x - 3) > 2
Solving for x gives:
x < 1
Therefore, the solution set for the inequality 2|x - 3| + 6 > 10 is:
x < 1 or x > 5
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The complete question:
Match each absolute value inequality on the left side with its solution set on the right
2|x - 3| + 6 > 10 - 2
I have attached my question please see picture
The required standard error of the mean is 2.4 units.
The standard error of the mean is calculated by dividing the population standard deviation by the square root of the sample size. In this case, the population standard deviation is 36 units and the sample size is 225. Therefore, the standard error of the mean is:
SE = σ / √n = 36 / √225
= 36 / 15 = 2.4 units
Therefore, the standard error of the mean is 2.4 units.
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Sketch a graph of a polynomial function with a positive leading coefficient and zeros at x = 4, 2, and
-1 (multiplicity 2).
The graph of the polynomial function with a positive leading coefficient and zeros at x = 4, 2, and -1 (multiplicity 2) is given by the image presented at the end of the answer.
How to define the functions?We are given the roots for each function, hence the factor theorem is used to define the functions.
The function is defined as a product of it's linear factors, if x = a is a root, then x - a is a linear factor of the function.
Considering the zeros of the function, the linear factors are given as follows:
x - 4.x - 2.(x + 1)² -> due to the zero of multiplicity 2 at x = -1.Considering the leading coefficient of a = 1, the function is defined as follows:
f(x) = (x - 4)(x - 2)(x + 1)²
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The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 80°, then what is the value of angle ABC? Give your answer in degrees (°). D E C A 80° B
The value of angle ABC in the equilateral triangle formed by points D, E, and C, given angle EAB is 80°, is 50°.
Let's solve the problem step by step:
In an equilateral triangle, all three angles are equal. Let's denote the measure of angle ABC as x.
Since the triangle is equilateral, angle BAC is also equal to x.
The sum of angles in a triangle is
=180°
Therefore, we can write the equation:
= x + 80 + x = 180.
Simplifying the equation, we have:
= 2x + 80 = 180.
Subtracting 80 from both sides:
= 2x = 100.
Dividing both sides by 2:
=x = 50.
Thus, angle ABC measures 50°.
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The complete question is:
The shaded triangle formed by points D, E and C is equilateral. If angle EAB is 80°, then what is the value of angle ABC? Give your answer in degrees (°).
the response times for a certain ambulance company are normally distributed with a mean of 13 minutes.95% of the response times are between 10 and 16 minutes
The average response time for the ambulance company is 13 minutes, with 95% of response times falling between 10 and 16 minutes.
The response times for a specific ambulance company follow a normal distribution with a mean of 13 minutes. This means that the majority of response times will cluster around the average of 13 minutes.
Furthermore, we know that 95% of the response times fall within the range of 10 to 16 minutes. This suggests that the response times are relatively consistent, with only a small percentage of outliers falling outside this range.
In summary, the average response time for this ambulance company is 13 minutes, and 95% of their response times fall between 10 and 16 minutes.
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PLEASE HELP ASAP Brainiest 100 points
Scale Factor
An engineer has a 60:1 scale drawing of a bridge. The dimensions of the scaled bridge deck are 36 inches by 4 4/5. What is the area of the actual bridge deck in square feet? 6,912 square feet
4,320 square feet
576 square feet
72 square feet
The actual bridge deck measures 4,320 square feet in size.
First, we need to convert the scaled dimensions to actual dimensions. Since the scale is 60:1, we need to multiply the scaled dimensions by 60 to get the actual dimensions.
The scaled length of the bridge deck is 36 inches, so the actual length is:
36 inches x 60 = 2,160 inches
The scaled width of the bridge deck is 4 4/5, or 24/5, inches. So the actual width is:
24/5 inches x 60 = 288 inches
To find the area of the actual bridge deck in square feet, we need to convert the actual dimensions to feet and then multiply:
Actual length in feet = 2,160 inches ÷ 12 inches/foot = 180 feet
Actual width in feet = 288 inches ÷ 12 inches/foot = 24 feet
Area in square feet = Actual length x Actual width = 180 ft x 24 ft = 4,320 square feet
Therefore, the area of the actual bridge deck in square feet is 4,320 square feet.
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If h(x) is a function created by combining two functions by multiplication and h(x) = 2x² + 5x-3, which could be true
of the two component functions?
The component functions must both be linear.
O The component functions must both be quadratic.
The component functions must have y-intercepts with different signs.
The component functions must have increasing or accelerating rates of change.
Answer:
[tex]h(x) = 2 {x}^{2} + 5x - 3[/tex]
[tex]h(x) = (2x - 1)(x + 3)[/tex]
-The component functions must both be linear.
-The component functions must have y-intercepts with different signs.
7. The sum of nine consecutive whole numbers is 99. What could be the largest of these whole numbers .
Answer:
15
Step-by-step explanation:
I'm going to be very honest with you; one of my kids had this problem recently and I remember the answer is 15.
99=15+14+13+12+11+10+9+8+7
So the largest number is 15.
The way we solved it:
Call the 1st number x. Each number after x is x+(a number) all the way up to x+8 (the 9th number in the series of 9 consecutive whole numbers):
x, x + 1, x + 2, x + 3, x + 4, x + 5, x + 6, x + 7 and x + 8
Add up those consecutive numbers (I know, it's kind of messy):
x + x + 1 + x + 2 + x + 3 + x + 4 + x + 5 + x + 6 + x + 7 + x + 8
Combine the like terms:
9x + 36 = 99
Subtract 36 from both sides:
9x = 63
Divide by 9 on both sides:
x = 7
So the largest number will be: x + 8
7+8 = 15
And then check that it works:
99=15+14+13+12+11+10+9+8+7
simplify please help i’ll give brainliest
Answer:
-2x^2 - 2x + 5
Step-by-step explanation:
Combine like terms (same variable and degree) to simplify
3x^2-5x^2+5x-7x+3+2
-2x^2-2x+5
Answer:
Combining like terms, we get:
-2x² - 2x + 6
The average price of a college math textbook is $151 and the standard deviation is $24. Suppose that 40 textbooks are randomly chosen. Round all answers to 4 decimal places where possible.
What is the distribution of
X? X ~ N( , )
For the group of 40, find the probability that the average price is between $152 and $155.
Find the third quartile for the average textbook price for this sample size. $
(round to the nearest cent)
For part b), is the assumption that the distribution is normal necessary? YesNo
(a) The distribution of X is X ~ N(151, 24)
(b) The probability that the average price is between $152 and $155 is 0.950
(c) The quartile for the average textbook price for this sample size is $167.2
(d) The assumption of normal distribution is necessary
(a) What is the distribution of X?Given that
Mean = 151
Standard deviation = 24
The distribution of X is represented as
X ~ N(Mean , Standard deviation)
So, we have
X ~ N(151, 24)
(b) The probability that the average price is between $152 and $155.The z-score is calculated as
z = (x - Mean)/Standard deviation
So, we have
z = (152 - 151)/24 and z = (155 - 151)/24
Evaluate
z = 0.042 and z = 0.167
So, we have
P = P(0.042 < z < 0.167)
Evaluate
P = 0.95044
Approximate
P = 0.950
(c) Finding the third quartileThis is calculated as
Q₃ = Mean + 0.675 * Standard deviation
So, we have
Q₃ = 151 + 0.675 * 24
Evaluate
Q₃ = 167.2
Hence, the quartile for the average textbook price for this sample size is $167.2
(d) Is the assumption necessaryYes, the assumption is necessary
This is because
The distribution has a sample size greater than 25 as required by the central limit theorem
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