1. For a population with u= 50 and u=8
A. Find the z score for each of the following x values.
X=54, x= 42, x= 62, x=48, x=52. X=34
B. find the score (x value) that corresponds to each of the following z=scores.
Z= 1.00, z= -0.50, z= 0.75, z= -0.25, z=1.50, z= -1.50
2. A sample has a mean of M=40 and a standard deviation of s=6. Find the z score for each of the following x values from this sample.
X= 44, x= 28, x =42, x= 50, x= 46, x= 37
3. For population with SD of o=8, a score of x= 44 corresponds to z= -0.50. What is the population mean?
4. In a population of exam scores, a score of x=48 corresponds to z= +1.00 and a score of x= 36 corresponds to z= -0.50. Find the mean and SD for the population.
A. X= 60 on an exam with u=50 and o= 20.
B. A score of x=40, on an exam with u= 45 and o =2; or a score of x = 60 on a exam with u=70 and 0=20.
C. A score of x=62, on a exam with u=50 and o=8, or of x=23 on an exam with u=20 and o=2.
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)
5. A psychology class consisting of 14 males and 36 females. If the professor selects names from the class list using random sampling:
A. What is the probability of the first name being 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?
6. What is sampling with replacement and why is it used?
7. 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 the left side of the line and find the proportion in the body.
a. z=2.20
b. z=1.60
c. z=-1.50
d. -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= -90 and z= +0.90
c. z= -1.50 and z= +1.50
9. 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 of the left
b. 40% in the tail of the right
c. 75% in the body on the left
d. 99% in the body on the right.
10. IQ test scores are standardized to produce a normal distribution with a mean of u=100 and a standard deviation of o=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
Average or normal intelligence: IQ between 90 and 109
i. 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.
ii. 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?
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MALES
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FEMALES
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|
Age
|
P (Death within one year)
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Number of Living
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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
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0.188644
|
12,862
|
3.68
|
0.146696
|
24,331
|
4.45
|