The Math 122 Midterm Exam is coming up. Suppose the exam scores are normally distributed with apopulation mean of 74.8% and a standard deviation of 15.1%.

Let's first create a simulation to observe the expected results for a class of Math 122 students. In Google Sheets, create 25 random samples of 24 students each. This means you should have 24 entries in each column, and you should be using columns A - Y. If you need a refresher for creating a random sample that is normally distributed, you can review the Technology Corner from Module 2 (Use NORMINV).

After creating your random samples, copy all the numbers then use the "Paste Values" option in Google Sheets to lock the numbers in place. Save your file as an .xlsx, then attach it here (File >> Download >> Microsoft Excel):

Question 1 Part 1 of 6Choose FileNo file chosen

Now find the mean of each sample. This can be done by going to the A26 cell and typing: =AVERAGE(A1:A24). You can then drag that formula over to the Y column to see the mean of each sample.

What is the highest mean? Use =MAX(A26:Y26)

What is the lowest mean? Use=MIN(A26:Y26)

Note: While there are no points associated with the attachment or the highest/lowest mean, points will be deducted for not completing this portion or doing it incorrectly. These should be used to help you understand the remainder of the problem.

What is the probability of a student getting a score of 90% or better? (Round to four decimal places.)

What is the probability of a class of 24 students having a mean of 90% or better? (Round to six decimal places.)

Explain, in your own words, why the answers to these two questions are drastically different. Your explanation should include each of the following:

• references to your simulation
• references to your calculations
• common sense explanation

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People generally believe that the mean body temperature is 98.60F.

Researchers at a university took a simple random sample of 178 healthy individuals and found these results:

• The distribution is approximately normal
• The sample mean is 98.24F
• The standard deviation is 0.59F

We want to determine whether these sample results differ from 98.60F by a significant amount. One way to make that determination is to study the behavior of samples drawn from a population with a mean of 98.60. In other words, we're going to assume the population mean really is 98.60. We're going to see what normal sample means would look like if the population mean really was 98.60.

Generate 25 samples of 178 individuals from a normally distributed population with a mean of 98.60 and a standard deviation of 0.59. This means each column should have 178 entries and you should be using columns A - Y. If you need a refresher on generating a random sample from a normally distributed population, review the Technology Corner from Module 2 (Use NORMINV). After generating the random samples, you should copy the numbers and then "Paste Values" so the random numbers don't keep regenerating.

Now find the mean of each column, like you did in the Question 1. Then find the minimum of all the means, like you did in Question 1.

Save your Google Sheets as an .xlsx file and attach it here (File >> Download >> Microsoft Excel):

Question 2 Part 1 of 6Choose FileNo file chosen

Keep in mind that your Google Sheets file is what samples would look like if the population mean really is 98.60.

What is the lowest sample mean you obtained?

Note: While there are no points associated with the attachment or the lowest mean, points will be deducted for not completing this portion or doing it incorrectly. These should be used to help you understand the remainder of the problem.

Based solely on the simulations, would it be reasonable to obtain a sample mean of 98.24?

• yes
• no

If we assume the population mean is 98.60 and the standard deviation is 0.59, what is the probability of a single person having a temperature of 98.24 or less? (Round to four decimal places.)

If we assume the population mean is 98.60 and the standard deviation is 0.59, what is the probability of obtaining a sample mean of 98.24 or less from a sample of 178 individuals? (Round to six decimal places.)

What can we say about the assumption that the population mean is 98.60? Explain your answer completely. Keep in mind:

• The simulation you completed was under the assumption that the population mean is 98.60.
• The calculations you completed in the last two portions were assuming the population mean is 98.60.
• The sample that produced a mean of 98.24 degrees was the actual, real data.