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.