Question

At a local restaurant, the amount of time that customers have to wait for their food is normally distributed with a mean of 18 minutes and a standard deviation of 4 minutes. Using the empirical rule, determine the interval of minutes that the middle 99.7% of customers have to wait.

Answer 1

The middle 99.7% of customers at the local restaurant wait between 6 to 30 minutes for their food, based on the empirical rule applied to a normal distribution with a mean of 18 minutes and a standard deviation of 4 minutes.

Step-by-step explanation:

The question involves using the empirical rule to determine the interval of minutes that the middle 99.7% of customers have to wait for their food at a local restaurant with a normally distributed waiting time. Since the empirical rule states that 99.7% of data within a normal distribution falls within three standard deviations from the mean, we calculate as follows:

• Mean (μ) = 18 minutes
• Standard Deviation (σ) = 4 minutes

For the middle 99.7%:

• Lower Bound = μ - 3σ = 18 - 3(4) = 18 - 12 = 6 minutes
• Upper Bound = μ + 3σ = 18 + 3(4) = 18 + 12 = 30 minutes

Therefore, the interval within which the middle 99.7% of customers wait is from 6 to 30 minutes.

Answer 2

99.7% of customers have to wait between 8 minutes to 30 minutes for their food.

Step-by-step explanation:

We are given the following in the question:

Mean, μ = 18 minutes

Standard Deviation, σ = 4 minutes

We are given that the distribution of amount of time is a bell shaped distribution that is a normal distribution.

Empirical Formula:

• Almost all the data lies within three standard deviation from the mean for a normally distributed data.
• About 68% of data lies within one standard deviation from the mean.
• About 95% of data lies within two standard deviations of the mean.
• About 99.7% of data lies within three standard deviation of the mean.

Thus, 99.7% of the customers have to wait:

`\mu -3\sigma = 18-3(4) = 6\\\mu +3\sigma = 18+3(4) = 30`

Thus, 99.7% of customers have to wait between 8 minutes to 30 minutes for their food.