Answered

suppose sat writing scores are normally distributed with a mean of 488 and a standard deviation of 113. a university plans to award scholarships to students whose scores are in the top 8%. what is the minimum score required for the scholarship? round your answer to the nearest whole number, if necessary.



Answer :

tutorconsortium270

The minimum score required for the scholarship is 646.765.

What is mean, variance and standard deviation ?

Standard deviation is a measure of the distribution of statistical data, whereas variance is a measure of how data points differ from the mean. The main distinction between the two is that whereas variance is expressed in squared units, standard deviation is expressed in the same units as the data's mean.

Calculation

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

In a set with mean  and standard deviation , the z-score of a measure X is given by:

Z = [tex]\frac{X - mean}{s.d.}[/tex]

In this problem, we have that:

mean  = 488 , s.d. = 113

What is the minimum score required for the scholarship?

Top 8%, which means that the minimum score is the 100-8 = 92th percentile, which is X when Z has a pvalue of 0.92. So it is X when Z = 1.405.

Z =  (X - mean) / s.d.

1.405 = (X - 488) / 113

X = (1.405 x 113) + 488

X =   646.765

the minimum score required for the scholarship is 646.765.

learn more about mean , standard deviation ,  variance here :

brainly.com/question/16241166

#SPJ4

Other Questions