A soft-drink bottler claims that, on average,
cans contain 12 oz of soda. Let x denote the
actual volume of soda in a randomly selected
can. Suppose that x is normally distributed
with = .16 oz. Sixteen cans are to be
selected and the soda volume determined for
each one; let x denote the resulting sample
average soda volume. Because the population
distribution is normal, the sample distribution
of x is also normal.
A) Give the mean and standard deviation of
the sampling distribution.
B) Find the probability that the sample
average soda volume falls between 11.94 and
C) In this sample, the sample average soda
volume is found to be 11.9 ounces. How
likely is this to happen if the true population
mean is 12 ounces?
In the library on a university campus, there is
a sign in the elevator that indicates a limit of
16 persons. Furthermore, there is a weight
limit of 2500 pounds. Assume the average
weight of students, faculty, and staff on
campus is 150 pounds, the standard deviation
is 27 pounds, and that the distribution of
weights of individuals on campus is
approximately normal. If a random sample of
16 persons from the campus is taken:
A) What is the expected value of the sample
mean of their weights.
B) What is the standard deviation of the
C) What average weight for those 16 people
will result in the total weight exceeding the
weight limit of 2500 pounds?
D) What is the probability that a random
sample of 16 persons on the elevator will
exceed the weight limit?
An airplane with room for 100 passengers has
a total baggage limit of 6000 pounds. Suppose
that the total weight of the baggage checked
by an individual passenger is a random
variable x with mean value 50 pounds and
standard deviation 20 pounds. If 100
passengers board a flight, what is the
probability that the total weight of their
baggage will exceed the limit?