Question

the life spans of a species of fruit fly have a bell-shaped distribution, with a mean of 32 days and a standard deviation of 5 days.
(a) the life spans of three randomly selected fruit flies are 34 days, 29 days, and 48 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 27 days, 37 days, and 42 days. using the empirical rule, find the percentile that corresponds to each life span.

(a) the z-score corresponding a life span of 34 days is 0.4.
(type an integer or a decimal rounded to two decimal places as needed.)

the z-score corresponding a life span of 29 days is -0.6.
(type an integer or a decimal rounded to two decimal places as needed.)

the z-score corresponding a life span of 48 days is 3.2.
(type an integer or a decimal rounded to two decimal places as needed.)

select all of the life spans that are unusual.
a. 29 days
b. 34 days
c. 48 days
d. none of the life spans are unusual.

(b) determine the percentiles using the empirical rule.
the 27 day fruit fly corresponds to a percentile of
the 37 day fruit fly corresponds to a percentile of
the 42 day fruit fly corresponds to a percentile of
(round to the nearest whole number as needed.)

Explanation:

Identify given parameters

Using the Empirical Rule Percentiles knowledge point

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LATEXBLOCK0
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Calculate standard deviations from the mean

Using the Empirical Rule Percentiles knowledge point

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LATEXBLOCK1
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Determine percentile for 27 days

Using the Empirical Rule Percentiles knowledge point

$$
LATEXBLOCK2
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Determine percentile for 37 days

Using the Empirical Rule Percentiles knowledge point

$$
LATEXBLOCK3
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Determine percentile for 42 days

Using the Empirical Rule Percentiles knowledge point

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LATEXBLOCK4
$$

Answer:

The 27 day fruit fly corresponds to a percentile of 16.
The 37 day fruit fly corresponds to a percentile of 84.
The 42 day fruit fly corresponds to a percentile of 98.