Question

A certain university maintains a colony of male mice for research purposes. The ages of the mice are normally distributed with a mean of 60 days and a standard deviation of 5.2. Assume you randomly sample 100 mice from the colony. How many will have an age of 65 or greater?

a. 44

b. 17

c. 94

d. 6

Answer #1

Solution:

Given, the Normal distribution with,

= 60

= 5.2

First we find P(an age of 65 or greater) i.e.P(X 65)

P(X 65) = P[(X - )/ > (65 - )/]

= P[Z > (65 - 60)/5.2]

= P[Z > 0.96]

= 1 - P[Z < 0.96]

= 1 - 0.8315 ( use z table)

= 0.1685

= 16.85%

Here , n = 100

16.85% of 100 will have an age of 65 or greater

Answer is
16.85 i.e. nearly **17**

**Option b is correct.**

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