Download Chapter7 1. Determine whether the sampling distribution of x is

Chapter7
1. Determine whether the sampling distribution of x is normal, approximately normal, or
unknown.
(a) Heights of American women aged 18 to 24 are distributed with mean 65.5 inches and
standard deviation 2.5 inches and the
 distribution is unknown. A random sample of
40 is selected.
(b) Average salaries for full-time associate professors in United States doctoral
departments of psychology are normally distributed with a mean of $71955 and a
standard deviation of $13513. A sample of size 20 is taken.
(c) A study involving the economic burden of congestive heart failure found that the
lengths of hospital stays for patients are not normally distributed with a mean of 7.8
days and a standard deviation of 9.1 days. A random sample of size 27 is taken.
(d) According to the Census Bureau’s 2002 American Community Survey, the average
travel time to work of workers 16 years and over living in Boston, MA, who did not
work at home, was 28.2 minutes with a standard deviation of 0.79 minutes. A sample
of 35 commute times is taken.
(e) Suppose that in a particular area, the average length of a hospital stay is 4.8 days with
a standard deviation of 3.0 days. A sample of 50 patients is taken.
.
2. If possible find the indicated probability. If not possible, explain why not
(a) The gestation time for human babies is assumed to be normally distributed with a mean
of 278 days and a standard deviation of 12 days. Suppose we take a sample of size 15.
What is the probability that the sample mean will be more than 270 days?
(b) Assume the fill amount of bottles of a soft drink is distributed with a mean of 2.0 liters
and standard deviation of 0.04 liter. If we take a random sample of 12 bottles, what is the
probability we will obtain a sample mean of 2.005 liters or more?
(c) A study involving the economic burden of congestive heart failure found that the lengths
of hospital stays for patients had a mean of 7.8 days with a standard deviation of 9.1 days.
A random sample of size 49 is taken. Find P(7.5< x < 8.5).
3. A random sample of size 100 is taken from a population having a mean 25 and a standard

deviation of 4. The shape of the population is unknown.
(a) Find the mean and the standard deviation of X .
(b) Find P[ X  25.65]
5. Assume that body temperatures of healthy adults are normally distributed with a mean of
98.2°F and a standard deviation of 0.62°F. Suppose we take a sample of eight healthy
adults. What is the probability that their mean body temperature will be greater than
98.4?
6. The package of Sylvania CFL 65-watt replacement bulbs that use only 16 watt claims that
these bulbs have a mean life of 8000 hours. Assume that the lives of all such bulbs have a
normally distribution with mean of 8000 hours and standard deviation of 400 hours. Let 𝑥̅
be the average life of 25 randomly selected such bulbs.
a. Find the mean and standard deviation of 𝑥̅ .
Find the probability that the mean life of a random sample of 25 bulbs is
b. Less than 7890 hours.
c. Between 7850 hours and 7910 hours.
d. Within 130 hours of the population mean.
e. Less than the population mean by 150 hours or more.
7. The Toyota Prius hybrid car is estimated to get an average of 50 miles per gallon (mpg) of
gas. However, the gas mileage varies from car to car due to a variety of conditions, driving
styles and other factors and has been reported to be as high as 70 mpg. Suppose that the
distribution of mpg for Toyota Prius hybrid cars has a mean of 50 mpg and standard
deviation 5.9 mpg. Find the probability that the mean mpg for 38 randomly selected Toyota
Prius hybrid cars is
a. More than 51.5
b. Less than 53
c. Between 48 and 51
8. Suppose the cable bills in US are normally distributed with mean of $82.69 and standard
deviation of $11.17. Let 𝑥̅ be the sample monthly cable bill for 23 randomly selected US
households with cable.
a. Find the mean and standard deviation of 𝑥̅ .
Find the probability that the sample mean life of a random sample of 25 bulbs is
b. Less than $80.
c. Between $75 and $85.
d. More than $90.