Download Problems from chapter7

Chapter7 Problems
1. Determine whether the sampling distribution of is normal, approximately normal, or
unknown.
(a) The times required for workers to complete a certain task are normally distributed
with a mean of 30 minutes and a standard deviation of 9 minutes. A random
sample of 35 workers is drawn.
(b) The useful lifetimes of a certain brand of light bulb are not normally distributed
with a mean of 250 hours and a standard deviation of 50 hours. A random sample
of 35 workers is drawn.
© A traffic study shows that the average number of occupants in a car is 2 and the
standard deviation is 0.35. A random sample of 35 workers is drawn.
(c) A random sample of size 36 are obtained from a population having a mean of 10
and a standard deviation of 9.
2. 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]
2. 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?
5. 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.
Find the probability that the sample mean life of a random sample of 25 bulbs is
(a) Less than $80.
(b) Between $75 and $85.
(c) More than $90.
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.
Find the probability that the mean life of a random sample of 25 bulbs is
(a) Less than 7890 hours.
(b) Between 7850 hours and 7910 hours.
Textbook: 7.24, 7.30