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Suppose that an accounting firm does a study to determine the time needed to complete one person’s tax forms. It randomly surveys 64 people. The sample mean is 26.75
hours. There is a known standard deviation of 4.75 hours. The population distribution is assumed to be normal.
a. Find the following values. (Enter exact answers)
i. Enter your answer
ii. Enter your answer
iii. Enter your answer
b. In words, define the random variables and :

…

Ask by Olson Smith. in the United States
Mar 29,2025

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a. Values:
i. Sample mean: 26.75 hours
ii. Standard deviation: 4.75 hours
iii. Sample size: 64
b. Definitions:
is the time (in hours) it takes to complete one person’s tax forms.
is the average time (in hours) it takes to complete tax forms for a group of 64 people.

Solución

a. Values:
i. The sample mean
ii. The standard deviation
iii. The sample size
b. Definitions of the random variables:
is a random variable representing the time (in hours) needed to complete one person’s tax forms.
is the sample mean of the time required to complete tax forms for a randomly selected sample of 64 people.

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Extra Insights

The sample mean (also known as ) is simply the average time taken from your surveyed individuals, which in this case is 26.75 hours. The standard deviation ( ) represents the variability in the time taken to complete tax forms, given as 4.75 hours. Finally, , the sample size, refers to the number of people surveyed, which is 64.
To clarify the random variables: represents the time taken by a single individual to complete their tax forms, while denotes the average time taken by the sampled group (in this case, 64 individuals) to complete their tax forms. Essentially, is about individuals, and provides collective insights from the group.

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