PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!
PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!! PLSSS HELPPPP I WILLL GIVE YOU BRAINLIEST!!!!!!

Answer:

a) The expected value is 75, the standard deviation is 3 and the shape is approximately normal.

b) 0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.

c) 0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.

d) 0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.

e) C = 81.51.

Step-by-step explanation:

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

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the zscore 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 pvalue, 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].

The scores on the test are normally distributed with a mean of 75 and a standard deviation of 15.

This means that [tex]\mu = 75, \sigma = 15[/tex]

a. What are the expected value, the standard deviation, and the shape of the sampling distribution of?

By the Central Limit Theorem, it will be approximately normal, with expected value [tex]\mu = 75[/tex] and standard deviation [tex]s = \frac{15}{\sqrt{25}} = 3[/tex].

b. What is the probability that the average aptitude test in the sample will be between 70.14 and 82.14?

This is the pvalue of Z when X = 82.14 subtracted by the pvalue of Z when X = 70.14.

X = 82.14

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

By the Central Limit Theorem

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

[tex]Z = \frac{82.14 - 75}{3}[/tex]

[tex]Z = 2.38[/tex]

[tex]Z = 2.38[/tex] has a pvalue of 0.9913.

X = 70.14

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

[tex]Z = \frac{70.14 - 75}{3}[/tex]

[tex]Z = -1.62[/tex]

[tex]Z = -1.62[/tex] has a pvalue of 0.0526

0.9913 - 0.0526 = 0.9387

0.9387 = 93.87% probability that the average aptitude test in the sample will be between 70.14 and 82.14.

c. What is the probability that the average aptitude test in the sample will be greater than 82.68?

This is 1 subtracted by the pvalue of Z when X = 82.68. So

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

[tex]Z = \frac{82.68 - 75}{3}[/tex]

[tex]Z = 2.56[/tex]

[tex]Z = 2.56[/tex] has a pvalue of 0.9948.

1 - 0.9948 = 0.0052

0.0052 = 0.52% probability that the average aptitude test in the sample will be greater than 82.68.

d. What is the probability that the average aptitude test in the sample will be less than 78.69?

This is the pvalue of Z when X = 78.69. So

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

[tex]Z = \frac{78.69 - 75}{3}[/tex]

[tex]Z = 1.23[/tex]

[tex]Z = 1.23[/tex] has a pvalue of 0.8907.

0.8907 = 89.07% probability that the average aptitude test in the sample will be less than 78.69.

e. Find a value, C, such that P(( x>C) = .015.

This is X when Z has a pvalue of 1 - 0.015 = 0.985. So X when Z = 2.17.

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

[tex]2.17 = \frac{X - 75}{3}[/tex]

[tex]X - 75 = 3*2.17[/tex]

[tex]X = 81.51[/tex]

So C = 81.51.

Answer:

Step-by-step

5. D

6. B

7.B

Answer:

I think 1/4

Step-by-step explanation:

1000% ÷ 4 =250%

Step-by-step explanation:

(250÷50)/(100÷50) = 5/2 when reduced to the simplest form.

Width of the enlarged photograph = 14 cm

Length of a small photograph = 6 cm

Width of a small photograph = 4 cm

Length of the photograph when enlarged = 21 cm

Let the width of the photograph when enlarged be x.

Which means :

[tex] = \tt 4 : 6 : : x : 21[/tex]

[tex] =\tt \frac{4}{6} = \frac{x}{21} [/tex]

[tex] =\tt 4 \times 21 = 6 \times x[/tex]

[tex] =\tt 84 = 6x[/tex]

[tex] =\tt x = \frac{84}{6} [/tex]

[tex] =\tt x = 14[/tex]

Thus, the value of x = 14

Therefore, the width of the enlarged photograph = 14 cm

Answer:

George is a good friend :)

Step-by-step explanation:

Answer:

1. 5 cm^2

2. 9.375 cm^2

3. 3/10 cm^2

4. 3/28 m^2

Step-by-step explanation:

Answer:

W

Step-by-step explanation:

Because the y-intercept is the line that passed through the y-axis

Answer:

Step-by-step explanation:

Answer:

if the period is a multiplication sign then its 135

Step-by-step explanation:

Answer:

135

Step-by-step explanation:

following the PEMDAS rule, of course

Answer:

AB = 10

CW = 8

angle BAD = 50

angle CDB = 65

angle DWA = 90

angle WCD = 25

Step-by-step explanation:

use the known facts that a rhombus = 360 degrees, pythagorean theorem, etc. if you want a full explanation lmk and i can edit my response

Answer:

8/40 = 20%

Step-by-step explanation:

Simply count the cubes in the blue rectangle, then count the cubes in the red rectangle. Divide red by blue, multiply that by 100. Thus giving your percent.

Answer:

b and d

Step-by-step explanation:

Answer: 84, 35

Step-by-step explanation:

12*7=84

5*7=35

84-35=49

The two numbers are 35 and 84

Let the two numbers be x and y

If the ratio are in 12: 5, hence:

x/y = 12/5

5x = 12y

x = 12y/5

If their difference is 49, then;

x - y = 49 .................. 2

12y/5 - y = 49

7y/5 = 39

7y = 49 * 5

y = 7 * 5

y = 35

Recall that x - y = 49

x = 49 + y

x = 49 + 35

x = 84

Hence the two numbers are 35 and 84

Learn more on equations here: https://brainly.com/question/14323743

Answer:

$45

Step-by-step explanation:

11.25/3= 3.75 x 12 = 45

Answer:

math          way  can help

Step-by-step explanation:

Answer:

C

Step-by-step explanation:

I got the answer C because if the estimated value of the tank is 50 and it gets drained it will only have 18 gallon in it

5%

3.36m inutos

2.24mi nutos

Answer:

3.45

Step-by-step explanation:

you have to do tihis then that

Step-by-step explanation:

mmmmmkkkkkkkkkkkkkkkkkk

Answer:

$2,874.19

Step-by-step explanation:

Hope this helps

Answer:

See attachment for graph

Step-by-step explanation:

Given

[tex]y = 2^x[/tex]

Required

Plot the graph

First, we list out possible values of x and y

When [tex]x = 0[/tex]:

[tex]y = 2^0 = 1[/tex]

When [tex]x= 1[/tex]:

[tex]y = 2^1 = 2[/tex]

When [tex]x =2[/tex]:

[tex]y = 2^2 = 4[/tex]

When [tex]x = 5[/tex]

[tex]y = 2^5 = 32[/tex]

So, we plot the graph by connecting the points of the above values.

See attachment for graph

Answer:

4) 7k² + 9k

= k(7k + 9)

5) x² - 25

= (x)² - (5)².

(a² - b²) = (a+b)(a-b)

= (x - 5)(x + 5)

Answer:

-5/3

Step-by-step explanation:

We can use the slope formula

m = ( y2-y1)/(x2-x1)

   = ( -3 -7)/(6-0)

   = -10 / 6

   = -5/3

Answer:

Option B. y – 3 = –1/7(x – 3)

Step-by-step explanation:

From the question given above, the following data were obtained:

Slope (m) = –1/7

Coordinate = (3, 3)

x₁ coordinate = 3

y₁ coordinate = 3

The equation of the line can be written as follow

y – y₁ = m(x – x₁)

y – 3 = –1/7(x – 3)

Answer:

x/3 + 6 = 14

Step-by-step explanation:

Answer:

x = 54

Step-by-step explanation:

Since both triangles are similar, therefore,

[tex] \frac{UV}{PQ} = \frac{VW}{QR} [/tex]

[tex] \frac{77}{66} = \frac{63}{x} [/tex]

[tex] \frac{7}{6} = \frac{63}{x} [/tex]

Cross multiply

[tex] 7*x = 63*6 [/tex]

[tex] 7x = 378 [/tex]

Divide both sides by 7

x = 54

Answer:

by point slope form

(y-5)/(x-2)=-2

Answer:

3x+y=16

x−y+4=8

4x−5+y=0

Answer:

16.1 + 6.1=22

that is not equal because it will give you 22.2

as the answer hope this helps

have a good day :)

Step-by-step explanation:

Answer:

7

Step-by-step explanation: