Class Time: Name:

Student Learning Outcome: The student will compare and contrast empirical data and a theoretical distribution. Find Probabilities for specific Normal Distributions

The Situation It is generally accepted that the mean body temperature is 98.6 degrees. If a sample of size 100 resulted in a sample mean of 98.3 degrees with a standard deviation of 0.64 degrees. Does this sample suggest that the mean body temperature is actually lower than 98.6 degrees?

Simulation: Using Minitab (Calc -> Random Data-> Normal), genrate 100 values from a normally distributed population with a mean of 98.6 degrees and a standard deviation of 0.63 degrees (using the sample standard deviation since the population deviation is unknown)

Data Collection Repeat the simulation 9 more times for a total of 10. Find the sample mean for each and record it below. (Requesting the data be stored in c2-c10 will generate the remaining 9 columns of data with one command. Then use Stats -> Basic Stats -> Display Descriptive and select all 10 columns.) ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________ ___________

Analyze the DataGiven the original data showed a mean temperature of 98.3 degrees, what might you conclude from your simulations? Is if likely to obtain a sample of size 100 with a mean temperature of 98.3 degrees? Explain.

Finding Probabilities for Normal Distribution Using Minitab, Calc -> Probability Distributions -> Normal, find the probabilities.Given a population with a normal distribution, a mean of 0, and a standard deviation of 1, find the probability of a value less than 1.25.__________________ Given a population with a normal distribution, a mean of 25, and a standard deviation of 3, find the probability of a value greater than 21.25.__________________ Given a population with a normal distribution, a mean of 100, and a standard deviation of 20, find the probability of a value between 87 and 122.__________________ Given a population with a normal distribution, a mean of 150, and a standard deviation of 35, what value has an area of 0.34 to the left?________________ Given a population with a normal distribution, a mean of 150, and a standard deviation of 35, what value has an area of 0.34 to the right?________________ Given a population with a normal distribution, a mean of 15, and a standard deviation of 2, what value has an area of 0.8 to the left?________________ Given a population with a normal distribution, a mean of 200, and a standard deviation of 15, which two values form the upper and lower boundary of the middle 80%?_______________________________