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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. Ordinarily entrance tests have a time limit. What maximum time limit should be set for this entrance test if it is desired to have no more than 8% of test takers fail to finish the test during that time limit? Round your answer to the nearest minute. Don't forget that we round all z values to two decimal places.

Respuesta :

Answer:

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

Step-by-step 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:

[tex]z_{score} = \displaystyle\frac{x-\mu}{\sigma}[/tex]

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

[tex]P( X < x) = P( z < \displaystyle\frac{x - 125}{18})=0.92[/tex]  

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

[tex]P(z < 1.405) = 0.92[/tex]

[tex]\displaystyle\dfrac{x - 125}{18} = 1.405\\\\x = 150.29 \approx 150[/tex]

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

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