Reference no: EM132843817
1. A normal distribution of scores has a mean of 62 and a standard deviation of 10. Find the z-scores corresponding to each of the following values:
a) A score that is 20 points above the mean.
b) A score that is 10 points below the mean.
c) A score that is 15 points above the mean
d) A score that is 30 points below the mean.
2. The Welcher Adult Intelligence Test Scale is composed of a number of subtests. On one subtest, the raw scores have a mean of 35 and a standard deviation of 6. Assuming these raw scores form a normal distribution:
a) What number represents the 65th percentile (what number separates the lower 65% of the distribution)?
b) What number represents the 90th percentile?
c) What is the probability of getting a raw score between 28 and 38?
d) What is the probability of getting a raw score between 41 and 44?
3. Scores on the SAT form a normal distribution with and .
a) What is the minimum score necessary to be in the top 15% of the SAT distribution?
b) Find the range of values that defines the middle 80% of the distribution of SAT scores. Find the z-scores
4. For a normal distribution, find the z-score that separates the distribution as follows:
a) Separate the highest 30% from the rest of the distribution.
b) Separate the lowest 40% from the rest of the distribution.
c) Separate the highest 75% from the rest of the distribution.
5. For the numbers below, find the area between the mean and the z-score:
a) z = 1.17
b) z = -1.37
6. For the z-scores below, find the percentile rank (percent of individuals scoring below):
a) -0.47
b) 2.24
7. For the numbers below, find the percent of cases falling above the z-score:
a) z = 0.24
b) z = -2.07
8. A patient recently diagnosed with Alzheimer's disease takes a cognitive abilities test and scores a 45. The mean on this test is 52 and the standard deviation is 5. What is the patient's percentile rank?
9. A fifth grader takes a standardized achievement test (mean = 125, standard deviation = 15) and scores a 148. What is the child's percentile rank?
10. Pat and Chris both took a spatial abilities test (mean = 80, std. dev. = 8). Pat scores a 76 and Chris scored a 94. What percent of individuals would score between Pat and Chris?
Name ______________________________ Date: _________________________ Period: ___________
Z-Score Practice Worksheet
11. A population has a μ= 137 and ?? = 17. What is the raw score corresponding to the following z-scores?
a. 145
b. 125
c. 15
12. A population has a μ= 100 and ?? = 30. What is the raw score corresponding to the following z-scores?
a. 2.0
b. -1.5
c. -0.2
13. Let z be a standard normal random variable. Compute each of the following problems.
a. P(z0.97)________________
b. P(z≤0.97) ________________
c P(z0.97) ________________
a. P(-0.97z0.97) ________________
b. P(z-5.0) ________________
f. P(z-5.0) ________________
14. Let X be a normal random variable with parameters μ= 8 and ?? = 3.5. Compute each of the following problems.
a. P(X0)
b. P(X15)
c. P(X 2)
15. Travel by us is an internet-based travel agency wherein customers can see videos of the cities they plan to visit. The number of hits daily is a normal distributed random variable with a mean of 1,000 and a standard deviation of 240. What is the probability of getting more than 900 hits on any given day?
16. The scoring of modern IQ is such that Intelligence Quotients (IQs) have a normal distribution of μ= 100 and ?? = 15.
a. What percent of people have an IQ of less than 80?
b. What percent of people have an IQ of greater than 120?
c. Mensa International is a non-profit organization that accepts only people with IQ score within the top 2%. What level of IQ qualifies one to be a member of Mensa?
17. The time spent by students working on a project is a normal random variable with parameters μ= 12 and
?? = 4.
a. What is the probability that the amount of the time spent on a project is less than 14 hours?
b. What is the probability that the amount of the time spent on a project is greater than 8 hours?