A biologist wants to estimate the life expectancy L of newly discovered species

Question

A biologist wants to estimate the life expectancy L of newly discovered species of beetle. To do this, she takes a sample of n insects and measures their life spans from birth to death. She then computes the average of these numbers. She believes that the life spans of these beetles are independent, normally distributed random variables with a mean of L and a variance of 1.5 days. How large should n be so that she be will 98% confident that the average life span computed from the sample is accurate to within plusminus 0.2 days of the actual life span L of the insects?

Explanation / Answer

n = ( Z * sigma / error ) ^2

alpha / 2 = 0.01 Z= 2.32

n = ( 2.32 * srqt 1.5 / 0.2 ) ^2

n = 201.84

n = 202

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