The life spans of a species of fruit fly have a bellshaped d

The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 30 days and a standard deviation of 4 days.

(a) The life spans of three randomly selected fruit flies are 34 days, 28 days, and 40 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.

(b) The life spans of three randomly selected fruit flies are 22 days, 38 days, and 34 days. Using the Empirical Rule, find the percentile that corresponds to each life span.

The z-score corresponding a life span of 34 days is

(Type an integer or a decimal rounded to two decimal places as needed.)

Solution

The life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 30 days and a standard deviation of 4 days.

The z score corresponding to 34 days is:

Z=(x-)/=(34-30)/4=1

The z score corresponding to 28 days is:

Z=(x-)/=(28-30)/4=-0.5

z score corresponding to 40 days is:

Z=(x-)/=(40-34)/4=1.5