Sampling Distribution of Means
1.
Name_____________________
Coal is carried from a mine in West Virginia to a power plant in New York in hopper cars on a long train.
The automatic hopper car loader is set to put 85 tons of coal into each car. The actual weights of coal
loaded into each car are normally distributed with a mean of 85 tons and standard deviation of 0.9 ton.
a.
What is the probability that one car chosen at random will have less than 84 tons of coal?
b. What is the probability that 20 cars chosen at random will have a mean load weight of less than 84
tons of coal?
2. The heights of 18-year-old men are approximately normally distributed, with mean 68 inches and standard
deviation 3 inches.
a.
What is the probability that an 18-year-old man selected at random is between 67 and 69 inches
tall?
b. If a random sample of ten 18-year-old mean is selected, what is the probability that the mean
height of the sample is between 67 and 69 inches?
3. Let x be a random variable that represents level of glucose in the blood (mg per deciliter of blood) after a
12-hour fast. The glucose level is approximately normal with a mean of 85 and a standard deviation of 25.
a.
What is the probability that a sample of 10 people have a mean glucose level less than 84.5?
b. What is the probability that a sample of 100 people have a mean glucose level less than 84.5?
4. Let x be a random variable that represents weights in kilograms of healthy adult female deer in December
in Mesa Verde National Park. It has a distribution that is approximately normal with mean of 63.0 kg and
standard deviation of 7.1 kg. What is the probability that a random sample of 50 doe weight less than 64.2
kg?
5. The distribution for the incubation time for the Allen hummingbird eggs has a mean of 16 days and
standard deviation of 2 days. Suppose that we have 30 eggs in an incubator. Let
incubation time for these eggs.
a.
What can we say about the shape of the probability distribution of
x be the average
x?
b. What is the mean of the distribution?
c.
What is the standard deviation of the distribution?
d. What is the probability that the average incubation for the 30 eggs is more than 17 days?
6. The taxi and takeoff time for commercial jets is a random variable x with a mean of 8.5 minutes and a
standard deviation of 2.5 minutes. You may assume that the jets are lined up on a runway so that one
taxies and takes off immediately after the other, and they take off one at a time on a given runway. What
is the probability that for 36 jets on a given runway total taxi and takeoff time will be less than 320
minutes?
7. The average fuel consumption for a Boeing 747 commercial jet in cruising position if 3213 gallons of jet
fuel per hour. Assume that the fuel consumption distribution is approximately normal with a standard
deviation of 180 gallons of jet fuel per hour. What is the probability that a sample of 20 jets used
between 3000 and 3500 gallons per hour?
8. Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the
watches have an average life of 38 months before certain electronic components deteriorate, causing the
watch to become unreliable. The standard deviation of watch lifetimes is 5 months. What is the
probability that a sample of 50 watches only lasts 37.4 months?