4.) For a population with = 50 and

a. Find the z-score for each of the following X values. (Note you should be able to find these values using the definition of a z-score. You should not need to use a formula or do any serious calculations.)

X= 54 X

X= 42 X= 34

b. Find the score (X value) that corresponds to each of the following z-scores. (Again, you should be able to find these values without any formula or serious calculations)

z = 1.00 z= 0.75 .50

z= -0.50 z= -0.25 z= -1.50

8.) A sample has a mean of and a standard deviation of s . Find the z-score for each of the following X values from this sample.

X= 44

X= 28 X= 50 X= 37

14.) For the population with a standard deviation of , a score of corresponds to

z = -0.50. What is the population mean?

18.) In a population of exam scores, a score corresponds to z = +1.00 and a score of corresponds to z = -0.50. Find the mean and the standard deviation for the population. (Hint: Sketch the distribution and locate the two scores in your sketch.)

22.) For each of the following, identify the exam score that should lead to the better grade. In each case, explain your answer.

a. A score of X = 56, on an exam with = 50 and ; or a score of X= 60 on an exam with = 50 and .

b. A score of X = 40, on = 45 and = 2; or a score of X = 60 with = 70 and = 20

c. A score of X= 62, on an exam with = 50 and ; or a score of on an exam with and = 2.

1. Review your response to item 22 above. Your principal is interested in seeing the relationship between performance on a summative (final) exam produced by the math teachers in your school and the state Common Core exam. How could z-scores be used to make this comparison for a selected group of 25 students in your school? (maximum 300 words)

Chapter 6:

2.) A psychology class consists of 14 males and 36 females, if the professor selects names from the class list using random sampling,

a. What is the probability that the first student selected will be a female?

b. If a random sample of n= 3 students is selected and the first two are both females,

what is the probability that the third student selected will be a male?

4.) What is sampling with replacement and why is it used?

6.) Draw a vertical line through a normal distribution for each of the following z-score locations. Determine whether the body is on the right or left side of the line and find the proportion in the body. (Note: the word body in this item refers to the bulk of the observations.)

a. z = 2.20

b. z = 1.60

c. z = - 1.50

d. z = - 0.70

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

a. z = - 0.50 and z = + 0.50

b. z = - 0. 90 and z = + 0.90

c. z = -1.50 and z = + 1.50

10.) Find the z-score location of a vertical line that separates a normal distribution as described in each of the following

a. 20% in the tail on the left

b. 40 % in the tail on the right

c. 75% in the body on the left

d. 99% in the body on the right

14.) IQ test scores are standardized to produce a normal distribution with a mean of and a standard deviation of = 15. Find the proportion of the population in each of the following IQ categories.

a. Genius or near genius: IQ greater than 140.

b. Very superior intelligence: IQ between 120 and 140.

c. Average or normal intelligence: IQ between 90 and 109.

1. For the following questions, a calculated probability of equal to or less than 0.05 is considered significant.

a.Is it significant to get a 12 when a pair of dice is rolled? Show evidence and discuss.

b.Assume a study of 500 randomly selected school bus routes revealed 480 arrived on time. Is it significant for a school bus to arrive late? Show evidence and discuss.

2. The following table is from the Social Security Actuarial Tables. For each age, it gives the probability of death within one year, the number of living out of an original 100,000 and the additional life expectancy for a person of this age. Determine the following using the table:

a. To what age may a female of age 60 expected to live on the average?

b. To what age is a male of age 70 expected to live on average?

c. How many 60-year old females on average will be living at age 61?

d. How many 70-year old males on average will be living at age 71?

MALES FEMALES

Age	P(Death within one year)	Number of Living	Life Expectancy	P(Death within one year)	Number of Living	Life Expectancy
10	0.000111	99,021	65.13	0.000105	99,217	70.22
20	0.001287	98,451	55.46	0.000469	98,950	60.40
30	0.001375	97,113	46.16	0.000627	98,431	50.69
40	0.002542	95,427	36.88	0.001498	97,513	41.11
50	0.005696	91,853	28.09	0.003240	95,378	31.91
60	0.012263	84,692	20.00	0.007740	90,847	23.21
70	0.028904	70,214	12.98	0.018938	80,583	15.45
80	0.071687	44,272	7.43	0.049527	594,31	9.00
90	0.188644	12,862	3.68	0.146696	24,331	4.45