Chapter 6
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Feb 20, 2024
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MAT 1450 – Introduction to Statistics
Chapter 6 Written Homework
Answer the questions below and upload it to the appropriate location in eLearn or, if in a face to face class, turn it in to your instructor by the date listed on the course calendar.
Learning Objectives
Understand the notation and interpret the parameters of a normal distribution
Standardize a normally distributed random variable
Calculate the mean and standard deviation of a normal distribution
Use the empirical rule for normal distributions to estimate probability
Use the normal distribution to compute probability
1.
True/False. Explain your choice. These normal distributions have the same area under their curves.
2.
Choose the normal distribution with the smallest standard deviation. Explain your choice.
3.
Which normal distribution has a larger z-score for the normally distributed random variable x=7? Show work to support your answer.
1
4.
Find the z-scores for the two normally distributed random variables, measured using different units of length.
a) x = 22 in, where X comes from N (15, 2.5)
b) y = 55.88 cm, where Y comes from N (38.1, 6.35)
5.
For which of the following distributions may we use the Empirical Rule? Why?
6.
The mean of a normally distributed data set is 110, and the standard deviation is 15. Draw a diagram of the situation and then answer the questions below.
a) Use the Empirical Rule to find the probability that a randomly selected data value is greater than 95.
b) Use the Empirical Rule to find the probability that a randomly selected data value is greater than 125.
7.
A psychologist wants to estimate the percent of people in a population with IQ scores between 80 and 125. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Draw a diagram of the situation and use the Empirical Rule
to estimate the percent.
8.
A psychologist wants to estimate the percent of people in a population with IQ scores between 83 and 151. The IQ scores of this population are normally distributed with a mean of 110 and a standard deviation of 15. Use your calculator to find P(83<x<151).
9.
The mean of a normally distributed data set is 118, and the standard deviation is 16.
Draw a diagram of the situation and then answer the questions below.
a) Find the probability that a randomly selected data value is greater than 140. Show your work.
b) Find the probability that a randomly selected data value is less than 90. Show your work.
10. In general, when solving a probability question about a normal distribution, how do you know when you use the Empirical Rule and how do you know when you must use your calculator?
2
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