Question

A particular leg bone for dinosaur fossils has a mean length of 5 feet with standard deviation of 3 inches. What is the probability that a leg bone is less than 62 inches

Answer 1

The probability of a leg bone measuring less than 62 inches is about 75% (74.86%).

Explanation:

To answer this question we can calculate the z-score, then use a table to look up a corresponding percentile using z tables.

The length is a random variable with mean = 60 in and standard deviation of 3 in and we are looking at a particular sample that 62 in long. That sample has the following z value:

`z = (62 - \mu)/(\sigma)=(62-60)/(3)=(2)/(3)\approx0.67`

The area under the normal distribution curve that corresponds to the z value of 0.67 (using a z table - available on line) is 0.7486. This is the probability that a random sample of a fossil leg length is less that our particular value 62 inches. Roughly speaking, the probability of a leg bone less than 62 in is about 75% (aka 75-th percentile).