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Chapter 6 Test B
Name: __________________________ Date: _____________
1. Mrs. Smith's reading class can read a mean of 175 words per minute with a standard
deviation of 20 words per minute. The top 3% of the class is to receive a special award.
What is the minimum number of words per minute a student would have to read in order
to get the award?
2. The standard deviation of a distribution is 20. If a sample of 225 is selected, what is the
standard error of the mean?
3. A survey of 250 lobster fishermen found that they catch an average of 32 pounds of
lobster per day with a standard deviation of four pounds. If a random sample of 30 lobster
fishermen is selected, what is the probability that their average catch is less than 31.5
pounds?
4. What is the z value such that 50% of the total area lies to the right of the curve in any
normal distribution?
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Chapter 6 Test B
5. What is the z value such that 85% of the total area lies to the left of it, as shown in the
figure below?
6. Find the probability P(z > 0.73) using the standard normal distribution.
7. If X is a normal random variable with mean 6 and standard deviation 3.0, then find the
value x such that P(Z > x) is equal to .7054, as shown below. (Note: the diagram is not
necessarily to scale.)
8. Find the probability P(Z < 0.22) using the standard normal distribution.
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Chapter 6 Test B
9. For a normal curve with mean 8 and standard deviation 6, which of the following parts of
the normal curve will have an area of approximately 34%?
10. If X is a normal random variable with standard deviation 3.50, and if the probability that
X is more than 10.83 is .1271 (as shown below), then what is the mean of X? (Note: the
diagram is not necessarily to scale.)
11. If X is a normal random variable with standard deviation 3.50, and if the probability that
X is less than 8.83 is .648 (as shown below), then what is the mean of X? (Note: the
diagram is not necessarily to scale.)
12. Find the probability P(–0.62 < z < –0.01) using the standard normal distribution.
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Chapter 6 Test B
13. If X is a normal random variable with mean 4, and if the probability that X is less than
5.76 is .72 (as shown below), then what is the standard deviation of X? (Note: the
diagram is not necessarily to scale.)
14. The mean weight of loads of rock is 43.0 tons with a standard deviation of 12.0 tons. If 9
loads are chosen at random for a weight check, find the probability that the mean weight
of those loads is less than 38.60 tons. Assume that the variable is normally distributed.
15. Find the probability P(–1.04 < z < 1.11) using the standard normal distribution.
16. The average gas mileage of a certain model car is 26 miles per gallon. If the gas mileages
are normally distributed with a standard deviation of 1.3, find the probability that a car
has a gas mileage of between 25.8 and 26.3 miles per gallon.
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Chapter 6 Test B
17. The average length of crocodiles in a swamp is 12 feet. If the lengths are normally
distributed with a standard deviation of 1.9, find the probability that a crocodile is more
than 11.5 feet long.
18. On an easy test, the mean score was 97 out of a possible 100 points. The distribution of all
test scores is mostly likely to be skewed in which way?
19. Find the probability P(0.26 < z < 1.33) using the standard normal distribution.
20. For a normal distribution with mean –9 and standard deviation 2, the value –10 has a z
value of what?
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