Download Chapter 6 Review A recent study of the life span of portable compact

Chapter 6 Review
1. A recent study of the life span of portable compact disc players found the average to be 3.7
years with a standard deviation of 0.6 year. If a random sample of 32 people who own CD
players is selected, find the probability that the mean lifetime of the sample will be less than 3.4
years. If the mean is less than 3.4 years, would you consider that 3.7 years might be incorrect?
2. Americans ate an average of 25.7 pounds of confectionary products each last year and spent an
average of $61.50 per person doing so. If the standard deviation for consumption is 3.75
pounds and the standard deviation for the amount spent is $5.89, find the following.
a. The probability that the sample mean confectionary consumption for a random sample
of 40 American consumers was greater than 27 pounds.
b. The probability that for a random sample of 50, the sample mean for confectionary
spending exceeded $60.00.
3. For the first 7 months of the year, the average precipitation in Toledo, Ohio, is 19.32 inches. If
the average precipitation is normally distributed with a standard deviation of 2.44 inches, find
these probabilities.
a. A randomly selected year will have precipitation greater than 18 inches for the first 7
months.
b.
Five randomly selected years will have an average precipitation greater than 18 inches
for the first 7 months.
4. The average cost of repairing an iPod is $120 with a standard deviation of $10.50. The costs are
normally distributed. If 15% of the costs are considered excessive, find the cost in dollars that
would be considered excessive.
5.
The average individual monthly spending in the United States for paging and messaging services
is $10.15. If the standard deviation is $2.45 and the amounts are normally distributed, what is
the probability that a randomly selected user of these services pays more than $15.00 per
month? Between $12.00 and $14.00 per month?
6. On a certain run of a commuter train, the average number of passengers is 476 and the standard
deviation is 22. Assume the variable is normally distributed. If the train makes the run, find the
probability that the number of passengers will be
a. Between 476 and 500 passengers.
b. Less than 450 passengers
c. More than 510 passengers
7. The average salary for graduates entering the actuarial filed is $40,000. If the salaries are
normally distributed with a standard deviations of $5000, find the probability that
a. An individual graduate will have a salary over $45,000.
b. A group of nine graduates will have a group average of over $45,000
8.
The average per capita spending on health care in the United States is $5274. If the standard
deviation is $600 and the distribution of health care spending is approximately normal, what is
the probability that a randomly selected person spends more than $6000? Find the limits of the
middle 50% of individual health care expenditures.
9. Use the standard normal distribution, find each probability.
a. P(0<z<2.07)
c.
P(-1.59<z<2.01)
b. P(-1.83<z<0)
d. P(1.33<z<1.88)
e. P(-2.56<z<0.37)
f. P(z>1.66)
g.
h. P(z>-1.19)
P(z<-2.03)
i. P(z<1.93)
j. P(z>-1.77)
10. Find the area under the standard normal distribution curve for each.
a. Between z = 0 and z = 1.95
b. Between z = 0 and z = 0.37
c. Between z = 1.32 and z = 1.82
e. Between z = -0.03 and z = 0.53
d. Between z = -1.05 and z = 2.5
f. Between z = 1.10 and z = -1.80
g. To the right of z = 1.99
h. To the right of z = -1.36
i. To the left of z = -2.09
j. To the left of z = 1.68