Find the probability a randomly selected mosquito lives longer than 13 days

Question

The lifespan of a mosquito is normally distributed with a mean of 17.4 days and a standard deviation of 2.4 days.

Answer 1

First, let's calculate the the z score which is (x - μ) / σ where x is the value being tested, μ the population mean, and σ the standard deviation.

(13 - 17.4) / 2.4 = - 1.83

The normal distribution table shows that this score has an area of 0.466 from 0 to -1.83. As you want the probability of living greater than 13 days, you must subtract 0.466 from 1.00 to get 0.534 which is the probability you want.