Question

data collected over a long period of time show that the length of time x to complete a particular college entrance test is normally distributed with an average of 125 minutes and a standard deviation of 18 minutes. identify the finishing time that corresponds to the 92nd percentile. round your answer to the nearest minute. don't forget that we round all z values to two decimal places.

Answer 1

Answer:Less than 8% of test takers will take longer than 150 minutes to finish the test.

Explanation:

We are given the following information in the question:

Mean, μ = 125 minutes

Standard Deviation, σ = 18 minutes

We are given that the distribution of length of time is a bell shaped distribution that is a normal distribution.

Formula:  

We have to find the value of x such that the probability is 0.92

 

Calculation the value from standard normal z table, we have,  

Thus, less than 8% of test takers will take longer than 150 minutes to finish the test.

Answer 2

Less than 8% of test takers will take lengthier than 150 minutes to complete the test.

What is percentile?

In statistics, a kth percentile exists as a score below which a provided percentage k of scores in its frequency distribution falls or a score at or below which a shared percentage falls. For example, the 50th percentile stands the score below which or at or below which 50% of the scores in the distribution may be located.

given the following data in the question:

Mean, μ = 125 minutes

Standard Deviation, σ = 18 minutes

We are provided that the distribution of length of time exists as a bell-shaped distribution that exists as a normal distribution.

Formula:

$z_{\text {score }}=\frac{x-\mu}{\sigma}$

To find the value of x such that the probability exists of 0.92

$P(X < x)=P\left(z < \frac{x-125}{18}\right)=0.92$

Estimate the value from the standard normal z table, we have,

P(z<1.405)=0.92

$&\frac{x-125}{18}=1.405$

$&x=150.29 \approx 150$

Thus, less than 8% of test takers will take lengthier than 150 minutes to complete the test.

To learn more about percentile refer to:

https://brainly.com/question/24245405

#SPJ2