The life spans of three randomly selected fruit flies are 34 days, 30 days, and

Question

The life spans of three randomly selected fruit flies are 34 days, 30 days, and 42 days. Find the z-score that corresponds to each life span. Determine whether any of these life spans are unusual.

For 34, z =

For 30, z =

For 42, z =

The life span of ? days is unusual.

The life spans of three randomly selected fruit flies are 29 days, 41 days, and 25 days. Using the Empirical Rule, find the percentile that corresponds to each life span.

For 29, approximately the ?th percentile.

For 41, approximately the ?th percentile.

For 25, approximately the ?th percentile.

For part (a), explain how you found which life span was considered unusual. For part (b), what do the percentiles mean in each situation?

Explanation / Answer

Mean 33 and sd = 4
So, z(34) = (34 - 33)/4 = 0.25
z(30) = (30 - 33)/4 = -0.75
z(42) = (42 - 33)/4 = 2.25
Life span of 42 days is quite unusual because for 42 days, z is more than 2.

percentile:
z(29) = -1
(-1) = 0.16; i.e. 16%

About 16% fruits flies in less than 29 days.

z(41) = 2
(2) = 0.97; i.e. 97%

About 97% fruits flies in less than 41 days.

z(25) = -2
(-2) = 0.03 ; i.e. 3%

About 3% fruits flies in less than 25 days.

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