Answer:
(a) 0.2033
(b) 0.0188
(c) 0.0004
(d) 0.095
Step-by-step explanation:
(a) the probability that a score at random is greater than 110 is obtained with a normal distribution of mean 100 and standard deviation 12 can be estimated using the z-table for Z = (110 - 100)/12 = 0.83
So P (X > 110) = P (Z > 0.83) = 0.2033
(b) Probability that a sample of 25 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{25} = 5[/tex]. That is a standard deviation of 12/5 = 2.4. which gives a Z-value of (105-100) / 2.4 = 2.08
P (X> 105) = P (Z > 2.08) = 0.0188
(c) Probability that a sample of 64 scores will have a mean greater than 105:
we use a standard distribution with the same mean (100) but the standard deviation reduced by a factor of [tex]\sqrt{64} = 8[/tex]. That is a standard deviation of 12/8 = 1.5. which gives a Z-value of (105-100) / 1.5 = 3.33
P (X> 105) = P (Z > 3.33) = 0.0004
(d) the probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105
This will be the addition of the two probabilities. We use a standard distribution with the same mean (100) but the standard distribution reduced by a factor of [tex]\sqrt{16} = 4[/tex]. That is a standard deviation of 12/4 = 3. which gives us two different Z values to study:
(105-100) / 3 = 1.67
and for X= 95 ==> Z = (95 - 100)/3 = - 1.67
P (X > 105) = P (Z > 1.67) = 0.0475
P (X < 95) = P (Z < -1.67) = 0.0475
which add up to: 0.095.
Using the normal distribution and the central limit theorem, it is found that there is a:
a) 0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
b) 0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
c) 0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
d) 0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
In a normal distribution 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]
It 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, which is the percentile of X. By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].In this problem:
Mean of 100, hence [tex]\mu = 100[/tex].Standard deviation of 12, hence [tex]\sigma = 12[/tex].Item a:
This probability is 1 subtracted by the p-value of Z when X = 110, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
[tex]Z = \frac{110 - 100}{12}[/tex]
[tex]Z = 0.83[/tex]
[tex]Z = 0.83[/tex] has a p-value of 0.7967.
1 - 0.7967 = 0.2033
0.2033 = 20.33% probability that a single score drawn at random will be greater than 110.
Item b:
Sample of 25, hence [tex]n = 25, s = \frac{12}{\sqrt{25}} = 2.4[/tex].
This probability is 1 subtracted by the p-value of Z when X = 105, hence:
[tex]Z = \frac{X - \mu}{\sigma}[/tex]
By the Central Limit Theorem
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{2.4}[/tex]
[tex]Z = 2.08[/tex]
[tex]Z = 2.08[/tex] has a p-value of 0.9812.
1 - 0.9812 = 0.0188
0.0188 = 1.88% probability that a sample of 25 scores will have a mean greater than 105.
Item c:
Sample of 64, hence [tex]n = 64, s = \frac{12}{\sqrt{64}} = 1.5[/tex].
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{1.5}[/tex]
[tex]Z = 3.33[/tex]
[tex]Z = 3.33[/tex] has a p-value of 0.9996.
1 - 0.9996 = 0.0004
0.0004 = 0.04% probability that a sample of 64 scores will have a mean greater than 105.
Item d:
Sample of 16, hence [tex]n = 16, s = \frac{12}{\sqrt{16}} = 3[/tex].
Both 105 and 95 are the same distance of the mean, so we find one probability, and multiply by 2.
[tex]Z = \frac{X - \mu}{s}[/tex]
[tex]Z = \frac{105 - 100}{3}[/tex]
[tex]Z = 1.67[/tex]
[tex]Z = 1.67[/tex] has a p-value of 0.9525.
1 - 0.9525 = 0.0475.
2 x 0.0475 = 0.095
0.095 = 9.5% probability that the mean of a sample of 16 scores will be either less than 95 or greater than 105.
A similar problem is given at https://brainly.com/question/24663213
What Quadrant is 4,-8 located in
Answer:
4
Step-by-step explanation:
1/4(x-2)+4=12 help please
Answer:
X = 34
Step-by-step explanation:
HELP PLS A carnival charges $2.50 per ride after an entrance fee.You paid a total of $22.50 after 6 rides.Find the total cost for 15 rides.
A bag contains 150 marbles. Some are blue, and the rest are white. There are 21 blue marbles for every 4 white marbles. . How many blue marbles are in the bag
Which statement is false? Explain.
A. An equiangular polygon has all angles congruent.
B. A regular polygon is both equilateral and equiangular.
C. An equilateral polygon has all sides congruent.
D. A polygon is concave if no diagonal contains points outside the polygon.
Answer: D. A polygon is concave if no diagonal contains points outside the polygon.
Explanation:
Choice A is true since "equiangular" means "equal angles"
Choice B is true since all sides are congruent, and all angles are congruent for a regular polygon
Choice C is true. The term "lateral" means "side".
Choice D is false because a convex polygon is one where all possible line segments contained in the polygon do not spill outside the polygon. Put another way, if points A and B are in a convex polygon, then every point on line segment AB is also in the polygon. Concave polygons don't have this feature. It is possible to draw a line segment where it spills outside the concave polygon.
a group of 12 runners each drink 64 ounces of water every day how many ounces of water will they drink in 45 days
factor 5x^2 + 10x + 5
If b^2=a then b is what of a?
Answer:
[tex]\huge\boxed{b = \sqrt{a}}[/tex]
Step-by-step explanation:
If we have an equation [tex]b^2 = a[/tex] and we want to find what b is in relation to a, we can change the equation so that we have b on one side and whatever is on the other side is what b is.
[tex]b^2 = a[/tex]
To isolate b, we can take the square root of both sides as taking the square root of something squared results in the base.
[tex]\sqrt{b^2} = \sqrt{a}[/tex]
[tex]b = \sqrt{a}[/tex]
So b is the square root of a.
Hope this helped!
Simplify
27^n+3 -6×3^3n+3/3^n×9^n+2
Answer:27^n+3–6*3^3n+3–n*9^n+2
Step-by-step explanation:
A car is going 50 miles per hour.
A rate that describes this would have units of?
А. miles and hours.
B. miles and cars.
C. hours only.
D. miles only.
miles and hours is the correct option.
NOT SURE BUT HOPE IT IS CORRECT AND HELPS YOU
What slope would make the lines
parallel?
y = 4x + 2
y = [?]x-4
Enter the number that belongs in the green box.
Answer:
4
Step-by-step explanation:
Parallel lines have the same slope and since the slope of the first line is 4 the second lines slope is also 4
Answer:
Step-by-step explanation:
Slopes of parallel lines are the same.
m = 4
Determine the unknown side of the similar triangle.
A)
2
B)
3
4
D)
5
Answer:
(C). 4
Step-by-step explanation:
Sides of the similar triangles are proportional.
if X ~ Y , then [tex]\frac{12}{6}[/tex] = [tex]\frac{8}{x}[/tex] ⇒ x = 4
simplify 3(12 - 8) + 5
Answer:
17
Step-by-step explanation:
The value of the given linear expression 3(12 - 8) + 5 is 17.
What is a linear equation?
A linear expression is an expression in which the highest power of the variable is always 1. If there is no variable, we can assume the power of the variable as 0.
Therefore, the variable x⁰ = 1.
Given linear expression:
3(12 - 8) + 5
= 3 × 4 + 5
= 12 + 5
= 17
Learn more about linear expression here: https://brainly.com/question/1955739
#SPJ2
The price of one share of a stock fell 4 dollars each day for 8 days. How much value did one share of the stock lose after 8 days?
Answer:
After 8 days, the stock lost 32 dollars.
Step-by-step explanation:
If 4 dollars fell every day for 8 days, it would be 32 dollars because 4*8 is 32.
Pls help me out I really need help
Answer: -0.8
Step-by-step explanation:
Evaluate 4p+q/p when p= -2 and q= -3
a) -11/2
b) 9/2
c) -9/2
d) 11/2
Answer:
D
Step-by-step explanation:
Answer:
d. 11/2
Step-by-step explanation:
(4p + q)/p
(4(-2) + (-3))/(-2) = (-8-3)/(-2)
11/2
Please help..............
Answer:
The first one.
Step-by-step explanation:
:)
if l || m,find the value of x, (8x + 20) (11x-31)
Answer:
x=17
Step-by-step explanation:
8x+20=11x-31
We simplify the equation to the form, which is simple to understand
8x+20=11x-31
We move all terms containing x to the left and all other terms to the right.
+8x-11x=-31-20
We simplify left and right side of the equation.
-3x=-51
We divide both sides of the equation by -3 to get x.
x=17
Answer:
17
Step-by-step explanation:
8x + 20 = 11x - 31
-8. -8
20 = 3× - 31
+31. +31
51 = 3x
/3. /3
x = 17
help me please i dont know what this is i cant think
Answer:
ahhhhh swear that's scary honestly
Which number is additive inverse of -4 1/4
Answer:
4 1/4
Step-by-step explanation:
the additive inverse is a number that when you add it with the number you already had, makes 0
-2 is the additive inverse of 2
so 4 1/4 is the inverse of -4 1/4
Identify the following data set:
The rates at which all of the cashiers scan products for a store on a study about the
cashiers for the day
Answer: Population
Step-by-step explanation:
Answer:
Population
Step-by-step explanation:
I just took the quiz
Find the value of x. Round to the nearest degree.
13.
22
14
Not drawn to scale
a. 47
b. 32
c. 40
d. 50
Answer:
32
Step-by-step explanation:
2) A farmhouse shelters 61 animals. Some are cows and some are ducks. Altogether there are
208 legs. How many of each animal are there?
Suppose that we have a sample space S = {E1, E2, E3, E4, E5, E6, E7}, where E1, E2, . . . , E7 denote the sample points. The following probability assignments apply:
P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.
Let A = {E1, E4, E6} B = {E2, E4, E7} C = {E2, E3, E5, E7}
Find the probability of the intersection of A and B.
Answer:
The required probability for the intersection of A & B = 0.25
Step-by-step explanation:
Given that:
Sample space S = {E1, E2, E3, E4, E5, E6, E7} and the probability of each sample points are:
P(E1) = .05, P(E2) = .20, P(E3) = .20, P(E4) = .25, P(E5) = .15, P(E6) = .10, and P(E7) = .05.
Also;
A = {E1, E4, E6}
B = {E2, E4, E7}
C = {E2, E3, E5, E7}
Then
P(A) = 0.05 + 0.25 + 0.10 = 0.4
P(B) = 0.20 + 0.25 + 0.05 = 0.5
P(C) = 0.20 + 0.20 + 0.15 + 0.05 = 0.6
The intersection of A and B are:
P(A ∩ B) = E4
P(A ∩ B) = 0.25
The required probability for the intersection of A & B = 0.25
Identify the angles that each have a measure of 88°.
Answer:
vdnchdbcdbchdbnhdbnhvbdjvjdsvhdfnjvdjvjdv
Step-by-step explanation:
If Michael can read 400 pages in 8 hours, how many pages can he read in 1 hour?
Step-by-step explanation:
He will read 50 pages in an hour
The amount of air pressure, (PSI) in the spare tire of a certain vehicle (Type A) brought for inspection are normally distributed with PSI of µ = 30 and σ = 4, and such spares tires with PSI below 25 are considered under-inflated.
The amount of air pressure, (PSI) in the spare tire of a certain vehicle (Type B) brought for inspection are normally distributed with PSI of µ = 27.7 and σ = 5.4, and such spare tires with PSI below 25 are considered under-inflated.
The PSI found in the spare tire of vehicle Type A and vehicle Type B does not depend upon the other type of vehicle, and every vehicle has 1 spare tire in it.
a. What is the probability that, for the next Type A vehicle and next Type B vehicle that are inspected, that BOTH vehicles have an under-inflated spare tire?
b. What is the probability that, for the next Type A vehicle and next Type B vehicle that are inspected, that there is a total of EXACTLY one under-inflated spare tire among these two vehicles?
Answer:
f
Step-by-step explanation:
A car moves at a speed of 30m/s to the west for 3hr. What is the displacement of the car in km?
Sam needs 7/8 cup mashed bananas and 5/6 cup mashed strawberries for a recipe. He wants to find whether he needs more bananas or more strawberries. How can he write 7/8 and 5/6 as a pair of fractions with the smallest common denominator?
Answer:
I don't no the answer i hope you
Find the slope-intercept form of the equation of the line that passes through the point P and makes angle with the positive x-axis
Answer:
The answer is "[tex]y= -x+7[/tex]"
Step-by-step explanation:
If [tex]\bold{\theta = 135^{\circ}}[/tex]
point: [tex]p=(2,5)[/tex]
Formula:
[tex]\to m= \tan \theta \\\\\to (y-y_1)= m(x-x_1)[/tex]
[tex]\to m= \tan \ 135^{\circ} = -1\\\\\to x_1= 2\\\\\to y_1=5[/tex]
Put the value in the above formula:
[tex]\to y- 5 = -1(x-2)\\\\\to y- 5 = -x+2\\\\\to x+y = 5+2\\\\\to x+y=7[/tex]
[tex]\to y= -x+7[/tex]