Question

A small city has two colleges, Eastern College and Gates Tech. At Eastern College, the time that a student spends studying outside of class each week is normally distributed with mean 22 hours and standard deviation 5.8. At Gates Tech, outside study time is normally distributed with mean 33 hours and standard deviation 8.7.

(a) What is the probability that a student at Eastern College spends between 13 and 18 hours a week studying outside of class?

(b) Durwood attends Eastern College, and studies 19 hours per week outside of class. Margaret attends Gates Tech, and studies 23 hours per week outside of class. Relative to the students at their own school, which person studies more outside of class? Explain your answer (and, as always, show your work).

Answer 1

(a) Probability that a student at Eastern College spends between 13 and 18 hours a week studying outside of class is,

We know that,

z₁₃ = (13 - 22)/5.8 = -1.5517

z₁₈ = (18 - 22)/5.8 = -0.6896

Therefore,

P(-1.5517 < z < - 0.6896) = P(z < -0.6896) - P(z < - 1.5517)

= 0.1849

​​​​​​ = 18.49%

(b)

The z score of Durwood is,

z = (19 - 22)/5.8

= -0.5172

The z score of Margaret is,

z = (23 - 33)/8.7

= -1.1494

Since the z score of Durwood is greater than Margaret, we can say that Durwood studies more outside of class.