Statistic Question (read below)

Question

Healthy 10-year-old domestic kittens have an average weight of 28.5 oz with standard deviations of 8.25 oz. The distribution is approximately normal. A kitten is designated as dangerously underweight when, at 10 weeks, it weighs less than 15 oz. You take a sample of five 10-week-old kittens. What proportion of healthy kittens will have a mean weight that is designated as dangerously underweight?

Answer 1

For this question I used the normalCDF function on the TI-83 and plugged in the -1E99 for the lower bound and -1.63636 for the upper bound. Which returned a probability of .0509.

-1.63636 was found by converting the distribution to the standard normal by saying (28.5-15)/8.25 = 1.63636.

You could also look this value up on a z-table that gives the normal distribution probabilities.

A sample of 5 kittens would then have 5(.0509)=.2544 kittens dangerously underweight.