Homework #9
Due 4/3/2003
1. High School dropouts make up 12.1% of all Americans aged 18 to 24.
A vocational school wants to do a survey to see how they could attract
dropouts to come to their school. The school surveys an SRS of 5,000 per-
sons from the entire population between the ages of 18 and 24.
a) What is the mean number of high school dropouts who will receive the
flyer? What is the standard deviation?
b) What is the probability that at least 1,000 dropouts will be contacted?
c) What is the probability that the SRS has a sample proportion ˆpthat is
within ±3% of the population proportion?
2. A company that owns and services a fleet of cars for its sales force
has found that the service lifetime of disc brake pads varies form car to car
according to a normal distribution with mean µ= 55,000 miles and stan-
dard deviation σ= 4500 miles. The company installs a new brand of brake
pads on 8 cars.
a) What is the mean and standard deviation of the sampling distribution of
the sample mean?
b) What is the probability that the sample mean is 51,800 or less?
c) The average life of the pads on the 8 cars turns out ro be x= 51,800.
The company takes the probability as evidence that the average lifetime of
the new brand of pads is less than 55,000 miles. Is this reasonable? Explain
why. What if the sample mean of the 8 cars were x= 45,800?
