Introduction to Statistics
Supplemental Instruction
Iowa State University / Leader: / Ben
Course: / STAT 226
Instructor: / Dr. Genschel
Date: / 28 September

THIS IS A SAMPLE PRACTICE EXAM BASED ON CONCEPTS THAT WILL BE COVERED ON THE ACTUAL EXAM. IN NO WAY SHOULD THIS PRACTICE EXAM BE TREATED AS A REALISTIC REPRESENTATION OF THE ACTUAL STAT 226 EXAMINATION

  1. A manufacturer desires to further research their production process by measuring the temperature of a machine after each product is manufactured. The temperature of the machine is measured for each product. The temperature of this machine tends to follow a distribution as follows, X~N(400, 102).

What is the population in this example?

What is the parameter of interest?

Describe a potential sample of this population.

What proportion of products are created between 385 and 406 degrees?

A random sample of measurements were taken over the course of a day. The temperature of the machine was recorded for 50 products. What is the mean and standard error for this sample?

What is the probability that one of the 50 product samples mean temperature was greater than 396 degrees in the sample distribution?

What happens to the standard error when the sample size is increased by 10? When decreased by 10?

  1. A company wants to know the average arm length of students that attend Iowa State. Assume that the population is normally distributed with the following distribution, X~N(25, 12)

What is the population in this example?

Describe a potential sample for this population.

What is the parameter of interest?

What would be an example of a statistic for a hypothetical sample?

What shoe size would correspond with the 67th percentile?

The University decides to perform an analysis and surveys 10 students. What would be the mean and standard error for the sample?

What is the probability that a sample size of 10 has a mean arm length of more than 25.7 inches??

  1. The average length of steel produced and sold by a steel mill is said to be 72 inches. The company manufacturing them is most interested in the average circumference. The population has a mean of 72 and a variance of 9. The distribution is not normally distributed.

What proportion of the steel beams are less than 74 inches?

Describe the way that a researcher could analyze the results and make a sample follow a normal distribution.

Assume that a sample of 40 steel rods are taken and this meets the requirements of the Central Limit Theorem.

A purchaser is considering creating a contract with the manufacturer. The purchaser wants the average length of the steel rods to be between 73 and 71 inches. What proportion of 40 steel rod orders will meet these specifications?

  1. What are two characteristics of a normal distribution?
  1. What is special about the Standard Normal Distribution?
  1. Interpret the following:

X ~ N(25, 52)

X ~ N(110, 152)

  1. The mean weekly salary paid to employees is $1100 with a standard deviation of $200.
  1. Assuming a normal distribution, what percentage of employees make more than $650 a week?
  1. If the lowest salary is $600 and the median salary is $1100, does a normal distribution appear appropriate?
  1. Use Table A to approximate the probability for the following.
  1. P(Z < 1.47)
  2. P(Z > -1.83)
  3. P(-1 < Z < 1.5)
  4. P(Z < 2.21)
  1. Use Table A to approximate the appropriate Z score for the following probabilities.
  1. P(Z < z) = .65
  2. P(Z > z) =.91
  1. There are two games, the scoring probability for each game is as follows A ~ N(24, 2) and B ~ N(10, 1). Which of the following is more likely? Scoring 22 or less in Game A or 11.5 or more in Game B?
  1. The average tire size is recorded and stored for analysis. The company manufacturing them is most interested in the average circumference. The population has a mean of 200 cm and standard deviation of 15 cm. The population is approximately normally distributed.

What proportion of tires are between 165 and 220 cm?

Assuming a sample size of 30, what is the mean and standard error of the sampling distribution?

What proportion of sample size 30 tires will have a mean of 197 cm or less?

  1. {8,9,5,11,12,7,6,4,9)

What is the mean?

Create a five number summary

Does the distribution appear to be skewed? Or is it symmetric?