1. The mean age of the viewers of a popular quiz show is 38.3 years with a standard deviation of 12.71 years.
a) What is the Z-score of a 25-year-old viewer?
b) What is the z-score of a 70-year-old viewer?
c) What is the z-score of a 40-year-old viewer?
d) What age range is within 1 standard deviation of the mean?
e) What age range is within 2 standard deviations of the mean?
f) What age range is within 1.3 standard deviations of the mean?

a) Approximately .

b) Approximately .

c) Approximately .

d) Approximately .

e) Approximately .

f) Approximately .

Step-by-step explanation:

The -score of a measurement gives the number of standard deviations between that measurement and the mean of the dataset.

For example, for this dataset, it is given that whereas . For a -year-old viewer, .

How far away is this observation from the mean of this population? .

The -score of this observation would be the approximate number of standard deviations that corresponds to this difference:

.

Similarly:

For , .

For , .

Separately adding and subtracting from would give the upper bound and the lower bound of the age range within standard deviation from the mean:

Similarly, for the interval within standard deviations from the mean:

For the interval within standard deviations from the mean:

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find the lower bound of the range.

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find the upper bound of the range.

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step-by-step explanation: