Assume that a randomly selected subject is given a bone density test. Those test scores are normally distributed with a mean of 0 and a standard deviation of 1. Find the probability that a given score is less than negative 0.84 and draw a sketch of the region.
Answers
Answer:
The "probability that a given score is less than negative 0.84" is [tex] \\ P(z<-0.84) = 0.20045[/tex].
Step-by-step explanation:
From the question, we have:
The random variable is normally distributed according to a standard normal distribution, that is, a normal distribution with [tex] \\ \mu = 0[/tex] and [tex] \\ \sigma = 1[/tex].We are provided with a z-score of -0.84 or [tex] \\ z = -0.84[/tex].Preliminaries
A z-score is a standardized value, i.e., one that we can obtain using the next formula:
[tex] \\ z = \frac{x - \mu}{\sigma}[/tex] [1]
Where
x is the raw value coming from a normal distribution that we want to standardize.And we already know that [tex] \\ \mu[/tex] and [tex] \\ \sigma[/tex] are the mean and the standard deviation, respectively, of the normal distribution.A z-score represents the distance from [tex] \\ \mu[/tex] in standard deviations units. When the value for z is negative, it "tells us" that the raw score is below [tex] \\ \mu[/tex]. Conversely, when the z-score is positive, the standardized raw score, x, is above the mean, [tex] \\ \mu[/tex].
Solving the question
We already know that [tex] \\ z = -0.84[/tex] or that the standardized value for a raw score, x, is below [tex] \\ \mu[/tex] in 0.84 standard deviations.
The values for probabilities of the standard normal distribution are tabulated in the standard normal table, which is available in Statistics books or on the Internet and is generally in cumulative probabilities from negative infinity, - [tex] \\ \infty[/tex], to the z-score of interest.
Well, to solve the question, we need to consult the standard normal table for [tex] \\ z = -0.84[/tex]. For this:
Find the cumulative standard normal table.In the first column of the table, use -0.8 as an entry.Then, using the first row of the table, find -0.04 (which determines the second decimal place for the z-score.)The intersection of these two numbers "gives us" the cumulative probability for z or [tex] \\ P(z<-0.84)[/tex].Therefore, we obtain [tex] \\ P(z<-0.84) = 0.20045[/tex] for this z-score, or a slightly more than 20% (20.045%) for the "probability that a given score is less than negative 0.84".
This represent the area under the standard normal distribution, [tex] \\ N(0,1)[/tex], at the left of z = -0.84.
To "draw a sketch of the region", we need to draw a normal distribution (symmetrical bell-shaped distribution), with mean that equals 0 at the middle of the distribution, [tex] \\ \mu = 0[/tex], and a standard deviation that equals 1, [tex] \\ \sigma = 1[/tex].
Then, divide the abscissas axis (horizontal axis) into equal parts of one standard deviation from the mean to the left (negative z-scores), and from the mean to the right (positive z-scores).
Find the place where z = -0.84 (i.e, below the mean and near to negative one standard deviation, [tex] \\ -\sigma[/tex], from it). All the area to the left of this value must be shaded because it represents [tex] \\ P(z<-0.84) = 0.20045[/tex] and that is it.
The below graph shows the shaded area (in blue) for [tex] \\ P(z<-0.84)[/tex] for [tex] \\ N(0,1)[/tex].
Related Questions
Domenic and Adriana are observing a hot-air balloon from two tracking stations on the ground.
The tracking stations are 6.0 km apart. From Domenic's point of view, the hot-air balloon is at an
angle of elevation of 72º. From Adriana's point of view, the angle of elevation is 58º.
Answers
Answer:
height of the balloon = 6.32 km
Step-by-step explanation:
The question wants us to find the height of the balloon .
They are observing the balloon from two tracking stations on the ground. The tracking stations are 6 km apart . From Dominic point of view the hair balloon is at an angle of elevation of 72° and from Adriana point of view the elevation is 58° . The illustration forms a triangle containing 2 right angles with a similar height.
To find the height we must find the hypotenuse of one of the right angle triangle. WE are given 2 angle and a side of 6 km. The third angle is 180 - 72 - 58 = 50°.
Using sin rule
6/sin 50° = b/sin 72°
cross multiply
6 sin 72° = b sin 50°
divide both sides by sin 50°
b = 6 sin 72°/sin 50°
b = 6 × 0.95105651629 /0.76604444311
b = 5.70633909777 /0.76604444311
b = 7.44909665372
b ≈ 7.45 km
The height can be found since we know the hypotenuse of one side of one of the right angle triangle.
sin 58° = opposite/hypotenuse
sin 58° = h/7.45
cross multiply
h = 7.45 × sin 58°
h = 7.45 × 0.84804809615
h = 6.31795831637
h ≈ 6.32 km
multiply your income by 2 to get your monthly income: $900
Answers
Answer:
monthly income=$900
the monthly income was multipled by 2
so, real income was, $900/2
=$ 450
so, $450×2=$900...
The real income is $400.
MultiplicationThe term multiplication refers to the product of two or more than two numbers.
How to find real income?Let us assume that the real income is x.
We have to multiply the real income by 2 to get the monthly income of $900.
This implies that [tex]x\times 2=\$900[/tex],
Solving the above expression, we will get
[tex]x\times 2=\$900\\x=\dfrac{900}{2} \\x=400[/tex]
So, the real income is $400.
Learn more about expression here-https://brainly.com/question/14083225
#SPJ2
Two similar circles are shown. The circumference of the larger circle, with radius OB, is 3 times the circumference of the smaller circle, with radius OA. Two circles are shown. The smaller circle has radius O A and the larger circle has radius O B. Radius OB measures x units. Which expression represents the circumference of the smaller circle with radius OA?
Answers
Answer:
{2 pi/3}x units
Step-by-step explanation:
i got it right on edg
Answer: Option B
{2 pi/3}x units
Step-by-step explanation:
An urn contains 11 balls, 3 white, 3 red, and 5 blue balls. Take out two balls at random, without replacement. You win $1 for each red ball you select and lose a $1 for each white ball you select. Let X be the random variable that notes the amount you win. Find the probability mass function (p.m.f.) of X.
Answers
Given: An urn contains 11 balls, 3 white, 3 red, and 5 blue balls.
You win $1 for each red ball you select and lose a $1 for each white ball you select.
Let X be the number of times you win.
The total number of ways to select 2 balls (order does not matter) =
The number of ways so that two balls are white (and [tex] X=-2):^3C_2=3 [/tex]
[tex]P(X=-2)=\dfrac{3}{55}[/tex]
The number of ways so that two balls are red (and [tex] X=2):^3C_2=3 [/tex]
[tex]P(X=2)=\dfrac{3}{55}[/tex]
The number of ways so that one ball is red, one is white (and [tex] X=0):^3C_1\times^3C_1=9 [/tex]
The number of ways so that two balls are blue (and [tex] X=0 [/tex] ): [tex] ^5C_2=(5 \cdot 4) / 2=10 [/tex]
i.e. [tex]P(X=0)=\dfrac{10+9}{55}=\dfrac{19}{55}[/tex]
The number of ways so that one ball is blue, one is white (and [tex] X=-1 [/tex] ): [tex] ^5C_1\times^3C_1=15 [/tex]
[tex]P(X=-1)=\dfrac{15}{55} =\dfrac{3}{11}[/tex]
The number of ways so that one ball is blue, one is red (and [tex] X=1 [/tex] ): [tex] ^5C_1\times^3C_1=15 [/tex]
[tex]P(X=1)=\dfrac{15}{55} =\dfrac{3}{11}[/tex]
Thus, the probability mass function (p.m.f.) of X would be ( in attachment) :
Two intersecting lines l and m form an angle of 56° with each other. The reflection of a point (–4, 1) along the line l followed by a reflection along line m will cause a ________ rotation. Question 18 options: A) 56° B) 112° C) 180° D) 28°
Answers
Answer:
B) 112°
Step-by-step explanation:
After the double reflection the point is effectively rotated by an amount that is double the angle between the lines of reflection:
2·56° = 112°
_____
In the attached, lines l and m are separated by 56°, as required by the problem statement.
use gauss-jordan elimination to solve the following linear system: -3x + 4y = -6 5x - y = 10
Answers
Answer:
See steps below on how to obtain the final solution
[tex]x=2\\y=0[/tex]
using Gauss elimination
Step-by-step explanation:
Let's write this system with the equations swapped since we want the largest value for the x dependence in the top row:
[tex]5x-y=10\\-3x+4y=-6[/tex]
Now let's scale the first equation by dividing it by 5 (the leading coefficient for x):
[tex]x-\frac{1}{5} y=2\\-3x+4y=-6[/tex]
now multiply row 1 by 3 and combine with row 2 :
[tex]3\,x-\frac{3}{5} y=6\\-3x+4y=-6\\ \\0+\frac{17}{5} y=0[/tex]
now replace the second row by this combination:
[tex]x-\frac{1}{5} y=2\\0+\frac{17}{5} y=0[/tex]
Now multiply the second row by 5/17:
[tex]x-\frac{1}{5} y=2\\0+} y=0[/tex]
multiply the bottom row by 1/5 and combine with the first row to eliminate the term in y:
[tex]x-\frac{1}{5} y=2\\0+\frac{1}{5} y=0\\ \\x-0=2[/tex]
Now we have the answer to the system:
[tex]x=2\\y=0[/tex]
An apple has a mass of 150g and a volume of 100cm³ Find its density in g/cm3? pls help
Answers
Answer:
1.5 g/cm³
Step-by-step explanation:
Density is g/cm³. This means that you have divide the mass by the volume.
(150 g)/(100 cm³) = 1.5 g/cm³
The density of the apple is 1.5 g/cm³.
Answer:
[tex] \boxed{\sf Density = 1.5 g/cm^3} [/tex]
Given:
Mass (m) = 150 g
Volume (V) = 100 cm³
To Find:
Density in g/cm³
Step-by-step explanation:
[tex]\sf Density = \frac{Mass (m)}{Volume (V)} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{15 \cancel{0}}{10 \cancel{0}} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \frac{15}{10} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 1.5 \: g/cm^3 [/tex]
Evaluate:-|137|+|13|
Answers
Answer:
The answer is 150
Step-by-step explanation:
I think what you mean with the numbers between the "I's" is absolute value. Any number is just that number, so the absolute value of -6, is 6. The absolute value of 24 is 24. That means it's simply 137+13, which is 150.
How can you write arithmetic and geometric sequences using recursive and explicit formulas modeled in a real world context?
Answers
Answer:
The answer is below
Step-by-step explanation:
They would be written like this:
Arithmetic Progression:
Explicit formula
Tn = a + (n-1) * d
Recursive formula
Tn = Tn-1 + d
Where a is the first term, d is the common differance and n is the number of terms.
Geometric Progression:
Explicit formula
Tn = a * r ^ (n-1)
Recursive formula
Tn = Tn-1 * r
Where r is common ratio
You are asked to lift something that is 15 kg. How many pounds is it? lbs
Answers
Answer:
33.0693394
Step-by-step explanation:
1 klio is 2.20462262,just mulipily by 15.
What is the interior angle measure of a convex decagon?
Answers
Answer:
The interior angle measure of a convex decagon is 144.
Step-by-step explanation:
The sum of the interior angle formula for a convex polygon is (n-2)180
where n is the number of sides.
A decagon has 10 sides.
10-2 = 8
8 times 180 = 1440
A decagon has 10 sides-10 angles.
To find the measure of each angle divide by 10.
1440/10=144
The interior angle measure of a convex decagon is 144.
what is the solution to this system of equations? I WILL GIVE 5 STARS ND BRAINLIEST
Answers
Answer:
(2, 6)
Step-by-step explanation:
The solution will be where the two lines intersect. From the graph, that point is (2, 6).
A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z)
Find the work done.
Answers
Answer:
Work done = 0 J
Step-by-step explanation:
work done= ∫ F. dr
= [tex]\int\limits^2_0 {x} \, dx[/tex] + [tex]\int\limits^2_2 {x} \, dx[/tex] + [tex]\int\limits^0_2 {x} \, dx[/tex] + [tex]\int\limits^0_0 {x} \, dx[/tex] + [tex]\int\limits^0_0 {y} \, dy[/tex] + [tex]\int\limits^5_0 {y} \, dy[/tex] + [tex]\int\limits^5_5 {y} \, dy[/tex] + [tex]\int\limits^0_5 {y} \, dy[/tex] + [tex]\int\limits^0_0 {z} \, dz[/tex] + [tex]\int\limits^1_0 {z} \, dz[/tex] + [tex]\int\limits^1_1 {z} \, dz[/tex] + [tex]\int\limits^0_1 {z} \, dz[/tex]
Work done= x²/2 + y²/2 + z²/2
Applying integral limits for entire pathway
Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2
Work done = 0 J
Three Savings accounts are advertised. - One savings account offers an APR of 2.43% compounded daily - another one offers an APR of 2.46% compounded monthly - A third offers an APR of 2.47% compounded annually Which one pays the most interest at the end of the one-year explain how you know your answers right
Answers
Answer:
2.46% monthly pays the most
Step-by-step explanation:
The formula for the effective annual rate of interest when nominal rate r is compounded n times per year is ...
r' = (1 +r/n)^n -1
For 2.43% compounded daily, the effective annual rate is ...
r' = (1 +0.0243/365)^365 -1 ≈ 2.4597%
For 2.46% compounded monthly, the effective annual rate is ...
r' = (1 +0.0246/12)^12 -1 ≈ 2.4879%
For 2.47% compounded annually, the effective annual rate is ...
r' = (1 +0.0247/1)^1 -1 = 2.47%
__
The account with an APR of 2.46% compounded monthly pays the most interest. (2.49% > 2.47% > 2.46% ⇔ monthly > annually > daily)
Mr. Lee left his fortune to his 3 sons, 4 daughters and his wife. Each son received twice as much as each daughter and his wife received $6000, which was a quarter of the money. How much did each son receive?
Answers
Hey there! :)
Answer:
$3600.
Step-by-step explanation:
If the wife received $6000 which is a quarter of the money, solve for the total amount of the fortune:
1/4x = 6000
Multiply both sides by 4:
x = $24000
We can begin by subtracting the wife's amount from the total:
24000 - 6000 = $18000
He has 3 sons and 4 daughters. Let 'x' represent the amount the daughters received, and '2x' the amount the sons received.
18000 = 3(2x) + 4(x)
Distribute and combine the terms:
18000 = 6x + 4x
18000 = 10x
Divide both sides by 10:
18000/10 = 10x/10
x = $1800. This is the amount that each daughter receives. Since the sons receive '2x':
2(1800) = $3600.
Answer:
He have 3 sons, 4 daughters and his wife.
His wife got $6000 from his fortune which is 1/4th of his fortune.
So.. 1/4x=$6000
Multiply both by 4, 1/4 multiply by 4 is 4/4=1,
So.. 1x=$24000
Now subtract the wife's share from the fortune
$24000-$6000=$18000
His have 3 sons and 4 daughters left, and his each son got twice more than each daughter
So... 18000=3(2x) +4(x)
18000 =6x +4x
18000=10x
x=18000÷10
=$1800 which is for each daughter
his each son got twice as much as each daughter
So.. 2 multiply by $1800
which is $3600.
so each son got $3600
If you are still not sure then add all the shares together
3(3600)+ 4(1800)+ 6000
=10800 +7200+ 6000
=$24000.
THERE YOU HAVE IT, THE ANSWER IS $3600
NGL even I didn't now but I got it from the answer above
So all the credit goes to the person who answered before me
Suppose that y is directly proportional to x and that y = 16 when x = 8. Find the constant of proportionality k.
Then, find y when x = 12.
Answers
Answer: 24
Step-by-step explanation:
Variation: y ∞ x
y = kx , where k is the constant of proportionality
now to find k, we substitute for y and x in the equation above
16 = 8k
therefore,
k = ¹⁶/₈
= 2.
Now, to find y , we move back to the equation above and substitute for x and k to get y
y = 12(2)
= 24
A monomial has only one variable. True or false
Answers
Answer:
False
Step-by-step explanation:
A monomial is an expression that contains one term.
An example can be 45ab.
There can be more than one variable.
Answer:
This is not always true.
Step-by-step explanation:
By definition, a monomial is an algebraic expression containing one term. Thus, the expression 3xy contains only one term but 2 variables.
4 − –5f = –66 f = _______
Answers
Answer:
f = -14
Step-by-step explanation:
given:
4 − (–5f) = –66
4 + 5f = -66 ( subtract 4 from both sides)
5f = -66 - 4
5f = -70 (divide both sides by 5)
f = (-70) / 5
f = -14
6th grade math , help me please :)
Answers
Answer:
A= 20x
B= 15n
C= 15x+ 9
D= a + 15
E= 9x + 3y
F= 10w + 10z
Step-by-step explanation:
Plz help thank you so much if you do The supplement of an angle is 30 degrees larger than twice its complement. Find the angle. A. 20 degrees B. 30 degrees C. 25 degrees D. 35 degrees Four times the complement of an angle is 9 degrees more than the supplement of the angle. Find the angle. A. 33 degrees B. 57 degrees C. 53 degrees D. 37 degrees
Answers
Answer: B) 30 degrees
Step-by-step explanation:
Look at this in a series of equations. The supplement of an angle(x) is 180 - x. The complement of an angle(x) is 90 - x. Thus the supplement of an angle(180 -x) is 30 degrees larger than twice its complement(90 - x). Thus, 180 - x = 30 + 2(90 - x)
180 - x = 30 + 180 - 2x
180 - x = 210 - 2x
x = 30
Answer: B) 57 degrees
Step-by-step explanation:
4(90-x) = 180 - x + 9
360 - 4x = 180 - x + 9
360 - 4x = 189 - x
360 = 189 + 3x
171 = 3x
57 = x
Hope it helps <3
(If it does, please mark brainliest, so close to next rank :) )
5÷5/6
6÷3/7
8÷5/8
5÷15/8
help please
Answers
Just division, fairly simple with or without a calculator.
Cereal costs 2.79 for 16.4 ounces. At this rate how much does 25 ounces of cereal cost? Round to the Nearest Cent.
Answers
Answer:
$4.25
Step-by-step explanation:
We can create a proportion to find how much 25 oz will cost:
[tex]\frac{2.79}{16.4}[/tex] = [tex]\frac{x}{25}[/tex]
We can cross multiply to find x.
16.4x = 69.75
x = 4.25
So, this means 25 ounces of cereal will be $4.25
help a girl out pls n thx!!
Answers
Answer:
The answer is option A.
50 degreesStep-by-step explanation:
To find angle C we use the cosine rule
That's
AB² = AC ² + CB ² - 2(AC)(CB)cos C
AC = 7.5
AB = 6
CB = 6.5
6² = 7.5² + 6.5² - 2(7.5)(6.5)cosC
36 = 56.25 + 42.25 - 97.5cos C
36 - 98.5 = - 97.5 cos C
-62.5 = - 97.5 cos C
cos C = -62.5 / - 97.5
C = cos ^-1 25/39
C = 50.1
The final answer is
C = 50°Hope this helps you.
• The average depth of the Hudson Bay is 305 feet. Climatologists were interested in seeing if the effects of warming and ice melt were affecting the water level. Fifty- five measurements over a period of weeks yielded a sample mean of 306.2 feet. The population variance is known to be 3.57. Can it be concluded at the .05 level of significance that the average depth has increased? (Use the Traditional method
Answers
Answer:
Step-by-step explanation:
We would set up the hypothesis test. This is a test of a single population mean since we are dealing with mean
For the null hypothesis,
H0: µ = 305
For the alternative hypothesis,
H1: µ > 305
This is a right tailed test
Since the population standard deviation is given, z score would be determined from the normal distribution table. The formula is
z = (x - µ)/(σ/√n)
Where
x = sample mean
µ = population mean
σ = population standard deviation
n = number of samples
From the information given,
µ = 305
x = 306.2
σ = 3.57
n = 55
z = (306.2 - 305)/(3.57/√55) = 2.49
Test statistic = 2.49
The calculated test statistic is 2.49 for the right tail and - 2.49 for the left tail
Since α = 0.05, the critical value is determined from the normal distribution table.
For the left, α/2 = 0.05/2 = 0.025
The z score for an area to the left of 0.025 is - 1.96
For the right, α/2 = 1 - 0.025 = 0.975
The z score for an area to the right of 0.975 is 1.96
In order to reject the null hypothesis, the test statistic must be smaller than - 1.96 or greater than 1.96
Since - 2.49 < - 1.96 and 2.49 > 1.96, we would reject the null hypothesis.
Therefore, at 5% level of significance, there is sufficient evidence to conclude that the average depth has increased.
The tree house will be 8 feet off the ground. Peter will hang a rope, with knots tied for foot holds. Each knot uses an additional 2 inches of rope. Write an expression for the length of the rope needed if Peter ties n knots and wants the rope to touch the ground. How many inches of rope are needed if there are 8 knots? Explain.
Answers
Answer:
Step-by-step explanation:
The answer is 56.
Answer:
The tree house is 8 feet off the ground, or 96 inches up because (8)(12) = 96. Each knot needs 2 extra inches, so the expression for the length of rope needed is 96 + 2n. If n = 8, then Peter will need 96 + 2(8) = 112 inches of rope.
Step-by-step explanation:
edge
Help ASAP! Which of the functions listen has the same graph as x + y = 11??
Answers
Answer:
f(x)=-x+11
Step-by-step explanation:
• A researcher claims that the average wind speed in a certain city is 8 miles per hour. A sample of 32 days has an average wind speed of 8.2 miles per hour. The standard deviation of the population is .6 miles per hour. At 5% level of significance is there enough evidence to reject the claim?
Answers
Answer:
Not reject null hypothesis since the p value is greater than 0.05
Step-by-step explanation:
We have the following:
z = (x ^ -m) / (sd / n ^ (1/2))
Let m be the mean that is 8, sd the standard deviation that is 0.6, n the sample size that is 32 and x the value to evaluate that is 8.2, replacing:
z = (8.2-8) / (0.6 / 32 ^ (1/2)) = 1.89
P (x> 8.2) = P (z> 1.89)
P (x> 8.2) = 1 - P (z <1.89)
We look for this value in the attached table of z and we have to:
P (x> 215) = 1 - 0.9713 (attached table)
P (x> 215) = 0.0287
since this is a two tailed test, the area of 0.0287 must be doubled the p value
the p value = 0.05794
Therefore, the decision is to not reject null hypothesis since the p value is greater than 0.05
Will give brainliest answer
Answers
Answer:
≈ 201 c m ^2
Explanation:
The area of a circle is given by formula:
π r ^2
π has a constant value of 3.14
And the radius of the circle is , half the diameter = d /2 = 16 /2 = 8 c m (assuming the unit to be in cm)
The area = π r ^2 = 3.14 × ( 8 ) ^2 c m ^2
= 3.14 × ( 64
) = 200.96 c m ^2
≈ 201 c m ^2
13r = 182 please explain
Answers
Answer:
r = 14
Step-by-step explanation:
We need to divide the equation by 13 so that we get just n one one side without any coefficients. Doing so we get r = 182 / 13 = 14.
Answer:
r = 14
Step-by-step explanation:
Well to find r we need to get it by itself and to do that we get rid of 13.
And to get rid of 14 we do 13r/13 and 182/13.
So 13r / 13 is r and 182/13 is 14.
So r = 14.
1
doyeisaac
21 hours ago
Mathematics
College
+5 pts
In the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each. A student has received homework scores of 7, 8, 7, 5, and 8 and the first two exam scores are 81 and 80. Assuming that grades are assigned according to the standard scale, where if the grade percentage is 0.9 or higher the student will get an A, and if the grade percentage is between 0.8 and 0.9 the student will get a B, and there are no weights assigned to any of the grades, is it possible for the student to receive an A in the class? What is the minimum score on the third exam that will give an A? What about a B?
Answers
Answer:
It is not possible for the student to receive an A grade in the class.
It is possible for the student to receive a B grade in the class.
Step-by-step explanation:
We are given that in the DBE 122 class, there are 350 possible points. These points come from 5 homework sets that are worth 10 points each and 3 exams that are worth 100 points each.
A student has received homework scores of 7, 8, 7, 5, and 8, and the first two exam scores are 81 and 80.
Firstly, we will calculate how many points have been scored by the student.
Number of possible points = 350
The points scored by the student in homework = 7 + 8 + 7 + 5 + 8 = 35 points.
The scores of the student on the two exams = 81 + 80 = 161 points
So, the total points scored by the students = 35 + 161 = 196 points.
As it is given in the question that if the grade percentage is 0.9 or higher then the student will get an A, i.e;
If the total possible points are 350 points; [tex]90\% \text{ of } 350 = \frac{90}{100}\times 350 = 315 \text{ points}[/tex]
This means that the student must have to score 315 points to get an A grade.
Till the second exam, the total points scored by the students are 196 points. If the student scored full 100 marks in the third exam, then the total points scored by the student will be = 196 + 100 = 296 points.
Since 296 < 315, this means that it is not possible for the student to receive an A in the class.
Also, it is given in the question that if the grade percentage is between 0.8 and 0.9 the student will get a B, i.e, the student must obtain a minimum of 80% to get B grade.
If the total possible points are 350 points; [tex]80\% \text{ of } 350 = \frac{80}{100}\times 350 = 280 \text{ points}[/tex]
This means that the student must have to score a minimum of 280 points to get a B grade.
Till the second exam, the total points scored by the students are 196 points. If the student scored full 100 marks in the third exam, then the total points scored by the student will be = 196 + 100 = 296 points.
Since 296 > 280, this means that it is possible for the student to receive a B grade in the class.