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For a population with a mean of µ = 100 and a standard deviation of σ = 12,

a. Find the z-score for each of the following X values.

X = 106, | X = 115, | X = 130, |

X = 91, | X = 88, | X = 64, |

b. Find the score (X value) that corresponds to each of the following scores.

z = -1.00, | z = -0.50, | z = 2.00 , |

z = 0.75, | z = 1.50, | z = -1.25, |

Chapter 6 #8

What proportion of a normal distribution is located between each of the following z-score boundaries?

8A

z = -0.50 and z = +0.50?

8B

z = -0.90 and z = +0.90

8C

z = -1.50 and z = +1.50

Chapter 6 #12

For a normal distribution with a mean of µ = 80 and a standard deviation = 20, find the proportion of the population corresponding to each of the following scores.

12A

Scores greater than 85

12B

Scores less than 100

12C

Scores between 70 and 90

Chapter 6 #14

IQ test scores are standardized to produce a normal distribution with a mean of µ = 100 and a standard deviation of σ = 12. Find the proportion of the population in each of the following IQ categories.

14A

Genius or near genius: IQ greater than 140

14B

Very superior intelligence: IQ between 120 and 140

14C

Average or normal intelligence: IQ between 90 and 109

Chapter 6 #18

Information from the Department of Motor Vehicles indicates that the average age of licensed drivers is µ = 45.7 years with a standard deviation of σ = 12.5 years. Assuming that the distribution of drivers’ ages is approximately normal,

a. What proportion of licensed drivers are older than 50 years old?

b. What proportion of licensed drivers are younger than 30 years old?

For a population with a mean of µ = 70 and a standard deviation of σ = 20, how much error, on average, would you expect between the sample mean (M) and the population mean for each of the following sample sizes”

a. n = 4 scores

b. n = 16 scores

c. n = 25 scores

6A

n = 6, σ = 20, σ_{M} **= **

6B

n = 16, σ = 20, σ_{M} =

6C

n = 25, σ_{M} **= **

If the population standard deviation is σ = 8, how large a sample is necessary to have a standard error that is:

a. less than 4 points?

b. less than 2 points?

c. less than 1 point?

Chapter 5 #8

A sample has a mean of M = 40 and s = 6. Find the z-score for each of the following X values from this sample.

X = 44, | X = 42, | X = 46, |

X = 28, | X = 50, | X = 37, |

Chapter 5 #12

A score that is 6 points below the mean corresponds to a z=score of z = -0.50. What is the population standard deviation?

Chapter 5 #14

For a population with a standard deviation of σ = 8, a score of X = 44 corresponds to z = -0.50. What is the population mean?

Chapter 5 #26

A sample consists of the following n = 6 scores:

2, 7, 4, 6, 4, and 7

a. Compute the mean and standard deviation for the sample.

b. Find the z-score for each score in the sample.

In the original distribution, X = 2, what is the new X value once transformed to a distribution with M = 50 and s = 10?

In the original distribution, X = 7, what is the new X value once transformed to a distribution with M = 50 and s = 10?

In the original distribution, X = 4, what is the new X value once transformed to a distribution with M = 50 and s = 10?

In the original distribution, X = 6, what is the new X value once transformed to a distribution with M = 50 and s = 10?