College Prep. Stats.
Sections 6.1 – 6.3 Quiz Review
Name: _____________________________________
1. Is the following an example of a uniform distribution?
For numbers 2 – 4, use the uniform distribution below. Round to four decimal places.
2. What is the probability that the random variable has a value greater than 2?
3. What is the probability that the random variable has a value less than 2.5
4. What is the probability that the random variable has a value between 4.1 and 7.4?
For numbers 5 and 6, assume that adults have IQ scores that are normally distributed with a mean of 100 and a standard
deviation of 15 (as on the Wechsler test).
5. Find the probability that a randomly selected adult has an IQ less than 90. Round to four decimal places.
6. Find the IQ score separating the top 16% from the others. Round to two decimal places.
7. Find the area of the shaded region.
Round to four decimal places.
8. Find the z score if the area of the shaded region is 0.0901.
Round to two decimal places.
9. If z is a standard normal variable, find the probability that z is greater than 0.59. Round to four decimal places.
Numbers 10 – 14 are multiple choice questions, circle the letter of the correct answer.
10. If z is a standard normal variable, find the probability that z lies between 0 and 3.01. (multiple choice)
a) P(0 < x < 3.01) = 0.4987
b) P(0 < z < 3.01) = 0.4987
11. If z is a standard normal variable, find the probability that z is less than 1.13. (multiple choice)
a) P(x < 1.13) = 0.8708
b) P(x > 1.13) = 0.1292
c) P(z < 1.13) = 0.8708
d) P(z > 1.13) = 0.1292
12. In a standard normal distribution, what are the values of µ and σ? (multiple choice)
a) μ = 0, σ = 1
b) μ = 1, σ = 0
c) μ = 1000, σ = 15
d) μ = 10, σ = 1.5
13. What feature do you use on your calculator to find the area under a normal curve? (multiple choice)
a) invNorm(area to the right, μ, σ)
c) invNorm(area to the left, μ, σ)
b) normalcdf (left, right, μ, σ)
d) normalcdf (right, left, μ, σ)
14. What feature do you use on your calculator to find a z score using a given area under a normal curve? (multiple choice)
a) normalcdf (left, right, μ, σ)
c) normalcdf (right, left, μ, σ)
b) invNorm(area to the left, μ, σ)
d) invNorm(area to the right, μ, σ)
For numbers 15 – 18, determine the probability. Assume z is a standard normal variable.
15. P(–1.53 < z < 1.22)
16. P(z < 0.57)
17. P(z > – 0.09)
18. P(z < –1.43)
19. Calculate z0.95. Round to two decimal places.
For numbers 20 – 25, you must show the set up and the final answer to get full credit. Round answers appropriately and attach units
when needed.
For numbers 20 and 21, use the following information
The Short club UK is for primarily men under 5’7” and women under 5’2”. This group is for short people to discuss the difficulties
and prejudices of being short. Men’s heights are normally distributed with a mean of 69 inches and a standard deviation of 2.8 inches.
Women’s heights are normally distributed with a mean of 63.6 inches and a standard deviation of 2.5 inches.
20. What is the probability of randomly selecting a man that could join the Short Club UK?
21. If the requirements are changed so that only the shortest 4% of men are eligible, what is the new maximum height for men?
22. Assume that children have IQ scores that are normally distributed with a mean of 99 and a standard deviation of 13 (as on the
Stanford-Binet test). Find the probability that a randomly selected child has an IQ between 87 and 112.
23. Assume that children have IQ scores that are normally distributed with a mean of 99 and a standard deviation of 13 (as on the
Stanford-Binet test). Find P22, which is the IQ score separating the bottom 22% from the top 78%.
24. The heights of six year olds are normally distributed with a mean of 46 inches and standard deviation of 2.9 inches. The Giant
Drop, a ride at Six Flags Great America, has a height requirement of 48 inches. What percent of six year olds can ride The Giant
Drop?
25. The heights of six year olds are normally distributed with a mean of 46 inches and standard deviation of 2.9 inches. The Giant
Drop, a ride at Six Flags Great America, has a height requirement of 48 inches. What height requirement would allow only the tallest
10% of six year olds to ride the Giant Drop?