The incomes in a certain large population of college teachers have a normal distribution with mean $75,000 and standard deviation $8,000. Sixteen teachers are selected at random from this population to serve on a committee. What is the probability that their average salary is more than $77,500?

Answers

Answer 1

Answer:

0.1056 = 10.56% probability that their average salary is more than $77,500.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal Probability Distribution:

Problems of normal distributions can be solved using the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the z-score of a measure X is given by:

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].

For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.

Mean $75,000 and standard deviation $8,000.

This means that [tex]\mu = 75000, \sigma = 8000[/tex]

Sample of 16

This means that [tex]n = 16, s = \frac{8000}{\sqrt{16}} = 2000[/tex]

What is the probability that their average salary is more than $77,500?

This is 1 subtracted by the pvalue of Z when X = 77500. So

[tex]Z = \frac{X - \mu}{\sigma}[/tex]

By the Central Limit Theorem

[tex]Z = \frac{X - \mu}{s}[/tex]

[tex]Z = \frac{77500 - 75000}{2000}[/tex]

[tex]Z = 1.25[/tex]

[tex]Z = 1.25[/tex] has a pvalue of 0.8944

1 - 0.8944 = 0.1056

0.1056 = 10.56% probability that their average salary is more than $77,500.


Related Questions

The answer to that question was 43.93 not 43.98

Answers

Answer: Ok, but can you tell me what you want me to help you with you just put “ The answer to that question was 43.93 not 43.98” and I don’t understand.

Step-by-step explanation:

Joanna has six beads that she wants to assemble into a bracelet. Two of the beads have the same color, and the other four all have different colors. How many different ways can Joanna assemble her bracelet? (Two bracelets are considered identical if one can be rotated and/or reflected to obtain the other.)

Answers

Answer:

Step-by-step explanation: six beads 2 same color and the rest diff so lets say the same are 2 blues and then we have a red, yellow, green, and orange just do 6*6 and you get 36.


Find the compound amount on an investment of $8,500 at 7.5% compounded daily for 3.5 years.

Answers

Answer:

Accrued Amount: 10955.51, Total Interest: 2455.51

Step-by-step explanation:

A = P(1+r/n)nt

CI = A-P

Where,

CI = Compounded interest

A = Final amount

P = Principal

t = Time period in years

n = Number of compounding periods per year

r = Interest rate

PLZ ANSWER NO FAKE LINKS AND DONT SAY I READY ISNT ALLOWED

Answers

Answer:

A. 266

Step-by-step explanation:

Answer:

266

Step-by-step explanation:

285+127-146=266

Tickets for the school play sell for $4 each. Which graph shows the relationship between the number of tickets solo
(x) and the total income from the tickets (y)?

Answers

Answer:

I do not see all the graphs but it would be the reverse of what is shown for A. graph. The tickets sold to total income would have to be a 1:4 ratio where every 4 dollar leap in the y-axis is a one point (1 unit change in x).

Step-by-step explanation:

A stapler company checked its inventory for defective products on a random sample of 750 staplers. The company identified that 200 staplers were defective.

To the nearest percent, what is a good estimate of the percentage of all staplers at the company that are defective?

Question 3 options:

27%


550%


4%

Answers

Answer is 27% because 200 / 750= .2666666

This question confuses me, and I am not understanding it.

Answers

Answer: As n increases, p increases.

The question is asking you about the equation of a line, p=2n-10

The equation of a line is y=mx+b

In this equation, m is the slope (how much you go up or down and then over)

In this equation, b is the y-intercept (where it intersects with the y line at 0)

Now with this knowledge, p=2n-10

P stands for y and N stands for x (its the same thing even if different)

2n means the m=2

Since the slope is positve it goes up 2 and then right 1

The y-int is -10

Now the options want to know what happens as n increases

Since the slope is positive when the x increases you know that the y increases so

As n increases, p increases.

(also i attached what the graph looks like)

I hope this explanation could help, please let me know if you do not understand still and if you could mark brainliest I would greatly appreciate it.

Answer: as n increases p increases

Step-by-step explanation:

What is the value of the expression below?
64^1/3​

Answers

21.33 is the answer because you have to multiply 64 times 1/3

Answer:4

Step-by-step explanation:

Just did this question

Chang knows one side of a triangle iS 13 cm. Which set of two sides is possible for the lengths of the other two sides
of this triangle?
• 5 cm and 8 cm
• 6 cm and 7 cm
• 7 cm and 2 cm
• 8 cm and 9 cm

Answers

Answer:

8 cm and 9 cm

Step-by-step explanation:

The rule for these types of problems is that the sum of the 2 shorter sides in a triangle is greater than the biggest side's length. If you think about it, it does seem sensible.

5+8 and 6+7 are both 13, but they aren't greater than the biggest side's length which is also 13.

7+2 is also wrong as it is 9, which is less than 13.

8+9= 17, and 17 is greater than 13.

So that's the answer.

Hope this helps! :)

Answer:

D. 8+9

Step-by-step explanation:

i did it

Identify the type I error and the type II error that corresponds to the given hypothesis. The proportion of people who write with their left hand is equal to 0.32. Which of the following is a type I​ error? A. Reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually different from 0.32. B. Fail to reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually 0.32. C. Fail to reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually different from 0.32. D. Reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually 0.32.

Answers

Answer:

Type 1 error :

D. Reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually 0.32.

Type 11 error :

C. Fail to reject the claim that the proportion of people who write with their left hand is 0.32 when the proportion is actually different from 0.32.

Step-by-step explanation:

A type 1 error is committed when a true null rejected. That is an incorrect rejection of a true null. Hence, by rejecting the claim that proportion ofbpop

Type 2 error is made when a false null is adopted. Here, we fail to reject a false null. In the scenario above, type 11 error will be made if we fail to reject the claim that proportion of People who write with their left hand is 0.32, when the proportion is correctly not 0.32

100 pts plz someone help asappp

Answers

∠1=45°

∠2=135°

∠3=45°

∠4=135°

Answer:

∠1=45°

∠2=135°

∠3=45°

∠4=135°

Step-by-step explanation:

someone help me pls i will give brainlist



write only answers

Answers

I hope it's clear enough.

complete the table for the given rule.

Rule:Y=x-3


Please help me and I need the answers​

Answers

Answer:

First blank = 4

Second blank = 4

Third blank = 10

Step-by-step explanation:

When you have the x value, just subtract 3 to get the y value, and when you have the y value, add 3 to get the x value.

Hopefully this helps- let me know if you have any questions!

Enter a linear equation that models the situation.
A drugstore sells pens for $1.30 each and notebooks for $3 each. The owner would like to sell $35 of
these items each day. Use p for the number of pens and n for the number of notebooks.
A linear equation that models the situation is
= 35.

Answers

Answer: 1.30p + 3n = 35

Step-by-step explanation:

answer : 1.30 + 3 then subtract that answer from 35

Four gardeners record the weight, in pounds, of 5 pumpkins they grew. Which statement about the weights of the pumpkins is true? Gardener Kylie Mark Todd Greg Pumpkin Weights (lbs) 20, 21, 33, 40, 29 14, 19, 45, 20, 22 15, 15, 15, 30, 22 33, 34, 36, 39, 33​

Answers

Answer:

Last Option: The range of weights for Greg's pumpkins is the least

Step-by-step explanation:

iReady Diagnostic

What is 4v7^3 in exponential form?

Answers

Answer:

7 3/4

Step-by-step explanation:

Could someone please help with this?

Answers

9514 1404 393

Answer:

  5.  88.0°

  6.  13.0°

  7.  52.4°

  8.  117.8°

Step-by-step explanation:

For angle A between sides b and c, the law of cosines formula can be solved to find the angle as ...

  A = arccos((b² +c² -a²)/(2bc))

When calculations are repetitive, I find a spreadsheet useful. It doesn't mind doing the same thing over and over, and it usually makes fewer mistakes.

Here, the side opposite x° is put in column 'a', so angle A is the value of x. The order of the other two sides is irrelevant.

__

Additional comment

The spreadsheet ACOS function returns the angle in radians. The DEGREES function must be used to convert it to degrees. The formula for the first problem is shown here:

  =degrees(ACOS((C3^2+D3^2-B3^2)/(2*C3*D3)))

As you can probably tell from the formula, side 'a' is listed in column B of the spreadsheet.

The spreadsheet rounds the results. This means the angle total is sometimes 179.9 and sometimes 180.1 when we expect the sum of angles to be 180.0.

enlarge the line by scale factor-2,with point (6,5)as the centre of enlargement.Mark the ends of your lines with crosses using the cross-drawing tool​

Answers

Dilation involves changing the size of a figure

The endpoints of the image are (-2,-1) and (6,1)

How to determine the coordinates of the image

The coordinates of the pre-image are give as:

(2,2) and (6,2)

The scale factor is given as:

k = 2

The center of dilation is given as:

(a,b) = (6,5)

The coordinates of the image are then calculated as:

[tex](x,y) \to (k(x -a) + a, k(y -b) + b)[/tex]

For (2,2), we have:

[tex](x,y) \to (2(2 -6) + 6, 2(2 - 5) + 5)[/tex]

[tex](x,y) \to (-2, -1)[/tex]

For (6,2), we have:

[tex](x,y) \to (2(6 -6) + 6, 2(2 - 5) + 5)[/tex]

[tex](x,y) \to (6, -1)[/tex]

Hence, the endpoints of the image are (-2,-1) and (6,1)

Read more about dilation at:

https://brainly.com/question/3457976

anyone help please it due today? ​

Answers

Step-by-step explanation:

QU (2,3( (1,-2)

3--2/2-1 = 5/1

Slope of qu = 5

(-1,4)(-3,0)

0-4/-3--1= -4/-2 = 2

rs = 2

Please HELP, I am struggling please help ASAP

Answers

9514 1404 393

Answer:

  $2.50

Step-by-step explanation:

The equation that describes Elizabeth's table can be found using the 2-point form of the equation for a line.

  y = (y2 -y1)/(x2 -x1)(x -x1) +y1

  y = (47.50 -27.50)/(3 -1)(x -1) +27.50

  y = (20.00)/2(x -1) +27.50

  y = 10x +17.50

Elizabeth's flat fee is $17.50. The difference between that and Mang's flat fee is ...

  |17.50 -20.00| = |-2.50| = 2.50

The absolute value of the difference between the flat fees is $2.50.

pls help

i’m so confused on this

Answers

Answer:

√(100)

Step-by-step explanation:

√(5) × √(20)

√(5 × 20)

√(100)

What is 3 3/10 + 2 1/10

Answers

As a decimal- 5.4

As an exact form- 24/5

As a Mixed number- 5 2/5

Hope this helped :T

PLease HELPPPpP someone who is good at math PLS

Answers

Answer:

I think it would be A not sure tho

Step-by-step explanation:

HAPPY EARTH DAY GUYS! :)

Answers

Answer:

THANK YOU! YOU TOO! :)

Step-by-step explanation:

Have a nice dayyyyyy <3

Answer:

HAPPY EARTH DAY!!!!

:)

Round 0.766 to the nearest 10th

Answers

Answer:

0.766 rounded to the nearest tenth = 0.8

Step-by-step explanation:

To round 0.766 to the nearest tenth consider the hundredths’ value of 0.766, which is 6 and equal or more than 5. Therefore, the tenths value of 0.766 increases by 1 to 8.

Answer:

The answer is 0.8 trust me

Write a scenario about a bank account to represent the number sentence:
-100 + 100 = 0.

Answers

Answer:

when i went to the bank i took out $100, then the next day i put $100 back into the bank

Step-by-step explanation:

Answer: I had no money in my bank account but i took out 100 dollars by getting a loan! So i had to pay that money back, when i next got paid i gave the bank 100 dollars to cover my debt!

Step-by-step explanation:

(Im almost positive this is right!)

20 Here is a list of five numbers.
98^53
98^64
98^73
98^88
98^91
Find the lowest common multiple of these five numbers.

Answers

We want to five the lowest common multiple of these 5 numbers. We will see that the lowest common multiple is:

[tex]98^{91}[/tex]

A multiple of a number N is any product between N and a positive integer. Here we want to get the smallest common multiple of the 5 numbers in the given set.

Here, the set is:

[tex]{98^{53}, 98^{64}, 98^{73}, 98^{88}, 98^{91}[/tex]

Remember the rule:

[tex]a^n*a^m = a^{n + m}[/tex]

Then we can see that:

[tex]98^{91} = 98^{91}*1 = 98^{88}*98^{3} = 98^{73}*98^{18} = 98^{64}*98^{27} = 98^{53}*98^{38}[/tex]

So:

[tex]98^{91}[/tex]

Is a common multiple of all the numbers in the set, and is the smallest common multiple because is equal to the largest number in the set.

If you want to learn more, you can read:

https://brainly.com/question/1055068

2. A model of a house is shown.
6x-4
+ 12x + 3
14x + 13
What is the perimeter, in units, of the model?
A. 32x + 12
B. 46x + 25
C. 50x + 11
D. 64x + 24

Answers

Answer:

the answer is c 50x +11

Step-by-step explanation:

The Perimeter of the model is (50x + 11).

What is Perimeter?

A shape's perimeter is calculated mathematically using the idea of perimeter. You sum together the lengths of all the sides to find the perimeter.

We have,

The two sides of the triangle are 6x - 4 units each.

The length of the rectangle is 14x + 13.

The width of the rectangle is 12x + 3.

So, the perimeter of the house

= (6x -4) + (14x + 13) + (12x + 3) + 12x + 3 + 6x -4

= 50x + 11

Thus, the perimeter is 50x + 11.

Learn more about Perimeter here:

https://brainly.com/question/6465134

#SPJ2

Fill in the blank will choose brain

Answers

Answer:

Below :)

Step-by-step explanation:

The difference of the means would be:

90 - 50 = 40

When finding difference you need to use subtraction.

The difference is 40

The MAD score is 10

"This difference is 4 times the value of the MAD of each data set."

A student needs to print pamphlets for an activities fair. If the printer takes 3 minutes to print a pamphlet, which inequality represents
the possible number of pamphlets, p, the student can expect the printer to print in more than 30 minutes?
.
O 3p 30

Answers

Answer:

3p <_30

Step-by-step explanation:

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