An investment website can tell what devices are used to access the site. The site managers wonder whether they should enhance the facilities for trading via “smart phones” so they want to estimate the proportion of users who access the site that way (even if they also use their computers sometimes). They draw a random sample of 200 investors from their customer. Suppose that the true proportion of smart phone users is 36%.
The proportion of adult women in the United Sates is approximately 51%. A marketing survey telephones 400 people at random.
a) What proportion of women in the sample f 400 would you expect to see?
b) How many women, on average, would you expect to find in a sample of this size? (Hint: Multiply the expected proportion by the sample size).
The investment website of Exercise 1 draws a random sample of 200 investors from their customers. Suppose that the true proportion of smart phone users is 36%.
a) What would the standard deviation of the sampling distribution of the proportion of smart phone users be?
b) What is the probability that the sample proportion of smart phone users is greater than 0.36?
c) What is the probability that the sample proportion is between 0.30 and 0.40?
d) What is the probability that the sample proportion is less than 0.028?
e) What is the probability that the sample proportion is greater than 0.42?
The proportion of adult women in the USA is approximately 51%. A marketing survey telephones 400 people at random.
a) What is the sampling distribution of the observed proportion that are women?
b) What is the standard deviation of that proportion?
c) Would you be surprised to find 53% women in a sample of size 400?
d) Would you be surprised to find 41% women in a sample of size 400?
e) Would you be surprised to find that there were fewer than 160 women in the sample? Explain.
According to the Gallup poll, 27% of U.S. adults have high levels of cholesterol. They report that such elevated levels “could be financially devastating to the U.S. healthcare system” and are a major concern to health insurance providers. According to recent studies, cholesterol levels in healthy U.S. adults average about 215 mg/dl with a standard deviation of about 30 mg/dl and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy U.S. adults is taken,
As in Exercise 9, cholesterol levels in healthy U.S. adults average about 215 mg/dl with a standard deviation of about 30 mg/dl and are roughly Normally distributed. If the cholesterol levels of a sample of 42 healthy US adults is taken, what is the probability that the mean cholesterol level of the sample
a) Will be no more than 215:
b) Will be between 205 and 225?
c) Will be less than 200?
d) Will be greater than 220?
Organizers of a fishing tournament believe that the lake holds a sizable population of largemouth bass. They assume that the weights of these fish have a model that is skewed to the right with a mean of 3.5 pounds and a standard deviation of 2.32 pounds.
a) Explain why a skewed model makes sense here.
b) Explain why you cannot determine the probability that a largemouth bass randomly selected (“caught”) from the lake weighs over 3 pounds.
c) Each contestant catches 5 fish each day. Can you determine the probability that someone’s catch averages over 3 pounds?
d) The 12 contestants competing each caught the limit of 5 fish. What’s the standard deviation of the mean weight of the 60 fish caught?
e) Would you be surprised if the mean weight of the 60 fish caught in the competition was more than 4.5 pounds? Use the 68-95-99.7 Rule.
Loans: Based on past experiences, a bank believes that 7% of the people who receive loans will not make payments on time. The bank has recently approved 200 loans.
a) What are the mean and standard deviation of the proportions of clients in this group who may not make timely payments?
b) What assumptions underlie your model? Are the conditions met? Explain.
c) What’s the probability that over 10% of these clients will not make timely payments?
Back to school? Best known for its testing program, ACT Inc., also compiles data on a variety of issues in education. In 2004 the company reported that the national college freshman-to-sophomore retention rate held steadily at 74% over the previous four years. Consider colleges with freshman classes of 400 students. Use the 68-95-99.7 Rule to describe the sampling distribution model for the percentage of those students we expect to return to that school for their sophomore years.
Back to school, again: Based on the 74% national retention rate described in Exercise 31, does a college where 522 of the 603 freshman returned the next year as sophomores have a right to brag that it has an unusually high retention rate? Explain.
Seeds. Information on a packet of seeds claims that the germination rate is 92%. What’s the probability that more than 95% of the 160 seeds in the packet will germinate? Be sure to discuss your assumptions and check the conditions that support your model.
Apples: When a truckload of apples arrives at a packing plant, a random sample of 150 is selected and examined for bruises, discoloration, and other defects. The whole truckload will be rejected if more than 5% of the sample is unsatisfactory. Suppose that in face 8% of the apples on the truck do not meet the desired standard. What’s the probability that the shipment will be accepted anyway?
Genetic defect: It’s believed that 4% of children have a gene that may be linked to juvenile diabetes. Researchers hoping to track 20 of these children for several years test 732 newborns for the presence of this gene. What’s the probability that they find enough subjects for their study?