Name: _____________________________________
Essential Statistics
Sampling Distribution of x WS
1) The army reports that the distribution of head circumference among soldiers is approximately
normal with mean 22.8 inches and standard deviation of 1.1 inches.
a) What is the probability that a random sample of 20 soldiers will have an average head
circumference that is greater than 23 inches?
b) What is the probability that a random sample of 20 soldiers will have an average head circumference that is
between 20 and 23 inches?
c) How many inches in circumference would the average of a random sample of 10 soldiers’ heads be if it were at
the 60th percentile?
2) A gasoline tank for a certain car is designed to hold 15 gallons of gas. Suppose the capacity of gas tanks are
normally distributed with mean of 15 gallons and standard deviation of 0.1 gallon.
a) What is the probability that a random sample of 5 cars with have an average tank size of at most 14.9
gallons?
b) What is the probability that a random sample of 5 cars with have an average tank size between 14.9 and 15.1
gallons?
c) How many gallons, on average, would a random sample of 10 cars’ tanks hold if it were at the 3rd quartile of the
distribution?
3) Suppose that for the population of students at a particular university, the time required to
complete a standardized exam is normally distributed with mean 45 minutes and standard deviation 5
minutes.
a) What is the probability that a random sample of 50 students would require an average of at least
47 minutes to finish the exam?
b) What is the probability that a random sample of 30 students would require an average of more than 42 minutes
but less than 47 minutes to finish the exam?
c) How much time, on average, should be allowed for the exam if we wanted 90% of the random samples of 20
students to be able to finish in the allotted time?
d) Which would have the greater probability; that a random sample of 50 students would require an average of at
least 47 minutes to finish the exam OR that a random sample of 10 students would require an average of at least
47 minutes to finish the exam? Explain without calculating the probabilities.