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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, what percentage of customers have to wait between 10 minutes and 26 minutes?

Respuesta :

Answer:

95% of the customers  have to wait between 10 minutes and 26 minutes

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 18 minutes

Standard Deviation, σ = 4 minute

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.

Now, we can write:

[tex]10 = 18-2(4) = \mu - 2(\sigma)\\26 = 18+2(4) = \mu + 2(\sigma)[/tex]

Thus, by empirical formula, 95% of the data lies within two standard deviations of the mean.

Thus, 95% of the customers  have to wait between 10 minutes and 26 minutes

raphealnwobi

95% of customers have to wait between 10 minutes and 26 minutes

What is an empirical rule?

The empirical rules states that for a normal distribution, 68% of the values are within one standard deviation from the mean, 95% of the values are within two standard deviation from the mean and 99.7% of the values are within three standard deviation from the mean.

Given a mean of 18 minutes and a standard deviation of 4 minutes. Hence:

95% are within two standard deviation = 18 ± 2(4) = (10, 26)

95% of customers have to wait between 10 minutes and 26 minutes

Find out more on empirical rule at: https://brainly.com/question/10093236

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