The life spans of a species of fruit fly have a bell-shaped distribution, with a

Question

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 5 days. (a) The life spans of three randomly selected fruit flies are 33 days, 28 days, and 43 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 40 days, 25 days, and 20 days. Using the Empirical Rule, find the percentile that corresponds to each life span. Select all of the life spans that are unusual A, 28 days B. 33 days c. 43 days D. None of the life spans are unusual. (b) Determine the percentiles using the Empirical Rule. The 40 day fruit fly corresponds to the th percentile. The 25 day fruit fly corresponds to theth percentile. The 20 day fruit fy corresponds to theth percentile. Type an integer or a decimal.)

Explanation / Answer

(a) The mean is 30 days and the standard deviation is 5 days.

28 and 33 are within one standard deviation.

43 is out of 2 standard deviations and is unusual.

(b) 40 days is +2 standard deviations and by empirical rule corresponds to 97th percentile.

25 days is -1 standard deviations and by empirical rule corresponds to 15th percentile.

20 days is -2 standard deviations and by empircal rule corresponds to 2nd percentile.

(Note: Sometimes percentiles are rounded. In case values are not accepted, enter 98, 16, 2)

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