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 33 days and a standard deviation of 5 (a) The life spans of three randomly selected fruit flies are 34 days, 28 days, and 49 days. Find the z-score that correspond of these life spans are unusual. (b) The life spans of three randomly selected fruit flies are 38 days, 43 days, and 23 days. Using the Empirical Rule, find the span. A. 28 days B. 34days C. 49 days D. None of the life spans are unusual. (b) Determine the percentiles using the Empirical Rule. The 38 day fruity corresponds to the th percentile. The 43 day fruit fly corresponds to the th percentile. The 23 day fruit fly corresponds to the th percentile. (Type an integer or a decimal)

Explanation / Answer

As per empirical rule,

a) P(X < 38)

= P(z < (38 - 33)/5)

= P(z < 1)

= 0.84

So,

The 38th day corresponding to the 84 th percentile.

Similarly,

b) P(X < 43)

= P(z < 2)

= 0.975

Hence,

The 43 day fruit corresponding to 97.5 th percentile.

c) P(X < 23)

= P(z < 23 - 33)/5)

= P(z < -2)

= 0.025

Hence,

The 23 day fruit corresponding to 2.5 th percentile.

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