Download Review Ch5 and Ch6

Review Ch5 and Ch6
1. A random variable x can assume five values: 0, 1, 2, 3, 4. A portion of the probability distribution is
shown here:
x
0
P(x) .1
1
??
2
.3
3
.2
4
.1
a. Find P(1)
b. Construct a probability graph for P(x).
c. Calculate the population mean, variance, and standard deviation.
2. One thousand tickets are sold at $1 each for a color television valued at $400. What is the expected
value of the gain if a person purchases one ticket?
3. If 80% of the people in a community have Internet access from their homes, use the Binomial Table to
find the following probabilities for a sample of 10 people.
a. At most 6 have Internet access.
b. Exactly 6 have Internet access.
c. At least 6 have Internet access.
d. Which event, a, b, or c, is most likely to occur?
4. Suppose 15% of the trees in a forest have severe leaf damage from air pollution. If 5 trees are selected
at random, Use the Binomial Probability Formula to find the probability that exactly 3 of the 5 selected
trees have severe leaf damage.
5. A die is rolled 480 times. Find the mean, variance, and standard deviation of the number of 2s that will
be rolled.
6. Find these probabilities for the standard normal random variable z:
a. P(z<2.35)
b. P(-1.47<z<0.85)
c. P(z<-3.02)
7. Find the z value such that the area under the standard normal distribution curve between 0 and the z
value is 0.2123.
8. Find the z value to the left of the mean so that 60.64% of the area under the distribution curve lies to
the right of it.
9. Each month, an American household generates an average of 28 pounds of newspaper for garbage or
recycling. Assume the standard deviation is 2 pounds. If a household is selected at random, find the
probability of its generating
a. Between 27 and 31 pounds per month.
b. More than 30.2 pounds per month.
Assume the variable is approximately normally distributed.
10. A contractor decided to build homes that will include the middle 80% of the market. If the average size
of homes built is 1810 square feet, find the maximum and minimum sizes of the homes the contractor
should build. Assume that the standard deviation is 92 square feet and the variable is normally
distributed.
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11. A population has   37 and   6 . For a random sample of size n=6,
a. Determine the mean of the sample means. (e.g.  x )
b. Determine the standard deviation of the sample means. (e.g.  x )
12. The average number of pounds of meat that a person consumes a year is 218.4 pounds. Assume that
the standard deviation is 25 pounds and the distribution is approximately normal.
a. Find the probability that a person selected at random consumes less than 224 pounds per year.
b. If a sample of 40 individuals is selected, find the probability that the mean of the sample will be less
than 224 pounds per year.
13. If a baseball player’s batting average is 0.32 (32%), find the probability that the player will get at most
26 hits in 100 times at bat. Use the normal approximation to find the probability.
14. When n=10 and p=0.5, use the binomial distribution table to find the probability that X=6. Then use the
normal approximation to find the probability that X=6.
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