Question

Suppose you are conducting a survey about the amount grocery store baggers are tipped for helping customers to their cars .for a similar simulated population with 50 respondents the population mean is $1.73 and the standard deviation is $0.657
about 68% of the sample mean fall with in the intervals $_______ and $________
about 99.7% of the sample mean fall with in the intervals of $-------- and $

Answer 1

Using the Empirical Rule and the Central Limit Theorem, we have that:

• About 68% of the sample mean fall with in the intervals $1.64 and $1.82.

• About 99.7% of the sample mean fall with in the intervals $1.46 and $2.

What does the Empirical Rule state?

It states that, for a normally distributed random variable:

• Approximately 68% of the measures are within 1 standard deviation of the mean.

• Approximately 95% of the measures are within 2 standard deviations of  the mean.

• Approximately 99.7% of the measures are within 3 standard deviations of the mean.

What does the Central Limit Theorem state?

By the Central Limit Theorem, the sampling distribution of sample means of size n has standard deviation $s = \frac{\sigma}{\sqrt{n}}$.

In this problem, the standard deviation of the distribution of sample means is:

$s = \frac{0.657}{\sqrt{50}} = 0.09$

68% of the means are within 1 standard deviation of the mean, hence the bounds are:

• 1.73 - 0.09 = $1.64.

• 1.73 + 0.09 = $1.82.

99.7% of the means are within 3 standard deviations of the mean, hence the bounds are:

• 1.73 - 3 x 0.09 = $1.46.

• 1.73 + 3 x 0.09 = $2.

More can be learned about the Empirical Rule at brainly.com/question/24537145

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