Question

emily earned a score of 550 on exam a that had a mean of 450 and a standard deviation of 100. she is about to take exam b that has a mean of 350 and a standard deviation of 50. how well must emily score on exam b in order to do equivalently well as she did on exam a? assume that scores on each exam are normally distributed.

Answer 1

392

Explanation:

use the z-score formula to convert the values.

z = (X - υ) / σ

where X is the test statistic, υ is the mean, σ is the standard deviation.

z = (550 - 450) / 100

= 1.

z score of 1 in z-table has an area of 0.84134.

for exam b:

0.84134 = (X - 350) / 50

X - 350 = 50 (0.84134) = 42.067

X = 42.067 + 350 = 392.067 ≈ 392.

Emily must score 392