Question

Suppose gre quantitative scores are normally distributed with a mean of 582 and a standard deviation of 149. A university plans to recruit students whose scores are in the top 9%. What is the minimum score required for recruitment? round your answer to the nearest whole number, if necessary.

Answer 1

The minimum score required for recruitment  is 782.

What is standard deviation?

The standard deviation in statistics is a measurement of how much a group of values can vary or be dispersed. A low standard deviation suggests that values are often close to the set's mean, whereas a large standard deviation suggests that values are dispersed over a wider range.

We have given that ,To get into top 9%,

μ = 582,  σ = 149

Let K =be the minimum score required for recruitment.

the values of K find as below

P(Z < ((K - μ) / σ)) = 1- 0.09

P(Z < ((K - 582) / 149)) = 0.91            ..(1)

where is standard normal variable

Look into standard normal table with prob.0.90  and find the correspond Z value.

Now,

P(Z < 1.341) = 0.91             ..(2)

now using equation (1) and (2) find value K

K=582+1.341*149

K=781.80

K=782

Hence, the minimum score required for recruitment  is 782.

To know more about standard deviation, click on the link

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