How can you use scale models to solve problems

The scores on the GMAT entrance exam at an MBA program in the Central Valley of California are normally distributed with a mean

Kaylis [27]

Answer:

58.32% probability that a randomly selected application will report a GMAT score of less than 600

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

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 normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

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 $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .

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

In this problem, we have that:

$\mu = 591, \sigma = 42$

What is the probability that a randomly selected application will report a GMAT score of less than 600?

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{600 - 591}{42}$

$Z = 0.21$

$Z = 0.21$ has a pvalue of 0.5832

58.32% probability that a randomly selected application will report a GMAT score of less than 600

What is the probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{50}} = 5.94$

This is the pvalue of Z when X = 600. So

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{5.94}$

$Z = 1.515$

$Z = 1.515$ has a pvalue of 0.9351

93.51% probability that a sample of 50 randomly selected applications will report an average GMAT score of less than 600

What is the probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600?

Now we have $n = 50, s = \frac{42}{\sqrt{100}} = 4.2$

$Z = \frac{X - \mu}{s}$

$Z = \frac{600 - 591}{4.2}$

$Z = 2.14$

$Z = 2.14$ has a pvalue of 0.9838

98.38% probability that a sample of 100 randomly selected applications will report an average GMAT score of less than 600

8 0

3 years ago

What types of driving behaviors help make a driver safer? Press Space to open If there is a group of 100 drivers and 50 take a s

olasank [31]

It should be noted that the driving behaviors that can make a driver safe include:

Complying with road rules.
Excellent sense of navigation.
Being patient and courteous towards others.
Be responsible and reliable.

<h3>Driving behaviors.</h3>

It should be noted that driver behavior simply means the characteristics band actions that a driver performs when driving.

In order to prevent accidents, it's important for drivers to comply with road rules, have an excellent sense of navigation, and be patient and courteous towards others.

Learn more about driving on:

brainly.com/question/1071840

8 0

3 years ago

enter the value of c when the expression 21.2x+c is equivalent to 5.3(4x-2.6). PLEASE GIVE ME AN EXPLANATION AS WELL. I DON’T WA

tamaranim1 [39]

Well, I will not just give you a straight answer, since I do not have the resources to currently do so. But as a tip, I would try the substitution method to get rid of the ‘x’ variable and just solve for ‘c’ like normal. Your main expression should look like this, I believe:

21.2x+c = 5.3(4x-2.6)

To substitute h the is out, you could write this if it feels better for you:

21x+c = y and 5.3(4x-2.6) = y

Hope this helps!

6 0

3 years ago

Write the equation of the line that passes through the points (-6,-6) and (-2,-4) help

Anit [1.1K]

Answer:

y=1/2x-3

Step-by-step explanation:

3 0

3 years ago

John builds a square dog pen that has an area of 81 square feet. He then builds a secondpen that has an area of 64 square feet.

GarryVolchara [31]

Given that John builds a square dog pen that has an area of 81 square feet;

$A_1=81ft^2$

4 0

1 year ago