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2. A survey conducted on campus found that the time spent on lunch is normally distributed with a mean of 44 minutes and a standard deviation of 7 minutes. Estimate the following: a. What’s the percentage of UCA students who spend between 30 and 44 minutes on lunch? b. What’s the percentage of UCA students who spend more than 51 mins on lunch? c. What’s the percentage of UCA students who spend less than 30 mins on lunch? d. What’s the percentage of UCA students who spend between 10 and 30 minutes on lunch?

Question

  1. A survey conducted on campus found that the time spent on lunch is normally distributed with a mean of 44 minutes and a standard deviation of 7 minutes. Estimate the following: a. What’s the percentage of UCA students who spend between 30 and 44 minutes on lunch? b. What’s the percentage of UCA students who spend more than 51 mins on lunch? c. What’s the percentage of UCA students who spend less than 30 mins on lunch? d. What’s the percentage of UCA students who spend between 10 and 30 minutes on lunch?
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Solution

To estimate the percentages, we can use the properties of the normal distribution.

a. To find the percentage of UCA students who spend between 30 and 44 minutes on lunch, we need to calculate the area under the normal curve between these two values.

First, we need to standardize the values using the formula z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.

For 30 minutes: z = (30 - 44) / 7 = -2

For 44 minutes: z = (44 - 44) / 7 = 0

Next, we can use a standard normal distribution table or a calculator to find the area between -2 and 0. This represents the percentage of UCA students who spend between 30 and 44 minutes on lunch.

b. To find the percentage of UCA students who spend more than 51 minutes on lunch, we need to calculate the area under the normal curve to the right of 51 minutes.

First, we standardize the value: z = (51 - 44) / 7 = 1

Next, we can use a standard normal distribution table or a calculator to find the area to the right of 1. This represents the percentage of UCA students who spend more than 51 minutes on lunch.

c. To find the percentage of UCA students who spend less than 30 minutes on lunch, we need to calculate the area under the normal curve to the left of 30 minutes.

First, we standardize the value: z = (30 - 44) / 7 = -2

Next, we can use a standard normal distribution table or a calculator to find the area to the left of -2. This represents the percentage of UCA students who spend less than 30 minutes on lunch.

d. To find the percentage of UCA students who spend between 10 and 30 minutes on lunch, we need to calculate the area under the normal curve between these two values.

First, we standardize the values:

For 10 minutes: z = (10 - 44) / 7 = -4.857

For 30 minutes: z = (30 - 44) / 7 = -2

Next, we can use a standard normal distribution table or a calculator to find the area between -4.857 and -2. This represents the percentage of UCA students who spend between 10 and 30 minutes on lunch.

This problem has been solved

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