1. A Department of Transportation report about air travel found that nationwide, 76% of all flights are on time. Base the following questions on 125 randomly selected flights. You may assume the only outcomes are that a flight is either late or is on time.
a) How many flights would you expect to be late ?
b) Calculate the standard deviation ?
c) What is the probability you will have exactly 80 flights on time ?
d) What is the probability you will have 20 or less flights that are late ?
e) What is the probability you will have more than 100 on time ?
2. Assume the cholesterol levels of adult American women are normally distributed with a mean of 190 mg/dL and a standard deviation of 26 mg/dL.
a) What percent of adult women do you expect to have cholesterol levels at least 200 mg/dL ?
b) What percent of adult women do you expect to have cholesterol levels between 150 and 170 mg/dL (include the boundaries) ?
c) Above what value are the top 15% of women's cholesterol levels ?
d) What level would represent the 10th percentile ?
3. The manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.
a. What is the probability that a randomly selected ball bearing will be acceptable ?
b. What does the acceptable range of the diameter need to be if you wanted to accept 98% of the ball bearings ?
4. A tire manufacturer believes the tread life of its snow tires can be described by a normal distribution with a mean of 32,000 miles and a standard deviation of 7000 miles. Find the probability (rounding to tenth of percent) that a randomly selected tire will have a tread life:
a. of at least 40,000 miles
b. of 30,000 or less miles
c. that last between 30,000 and 35,000 miles (include the boundaries)
d. In planning a marketing strategy, a local tire dealer wants to offer a refund to any customer whose tires fail to last a certain number of miles. However, the dealer doesn't want to take too big a financial risk with this guarantee. If the dealer is willing to give refunds to no more than 1 out of every 50 tires sold, for what mileage can he guarantee each tire to last ?
e. Find the probability that 50 randomly chosen tires will have a mean tread wear of greater than 35,000 miles ?
5. A final exam in Sociology has a mean of 72 and a standard deviation of 9.2. If 35 students are randomly selected, find the probability that that the mean of their test scores will be greater than 76.
6. A purchasing agent at the Kelly Bread Company wants to estimate the mean daily usage of rye flour. She takes a sample for 50 straight days and finds that the sample mean is 180 pounds with a sample standard deviation of 38.5 pounds.
a) State the 90% confidence interval for the mean.
b) State the margin of error
7. A high school counselor is interested in the percentage of students who will be going to college. She randomly picks 60 students and finds that 53 will be going to college. Use a 95% confidence level to find the population proportion.
a) State the 95% confidence interval for population proportion.
b) State the margin of error
8. In a preliminary study, the sample standard deviation for the duration of a particular back pain suffered by patients was 18.0 months. How large a random sample is needed to construct a 90% confidence interval so that an estimate can be made within 2 months of the actual duration ?