Question

*Please show your work

*Be sure to round z-values to 2 decimal places and round any probabilities to 4 decimal places

*If doing a hypothesis test, be sure to sure state the Ho and Ha, you may choose the p-value or rejection region approach to hypothesis testing, unless otherwise noted in the question.

*If you need to use the normal approximation, be sure to show the appropriate steps.

1. A survey of U.S. adults found that 8% say their favorite sport is auto racing. You randomly select 400 U.S. adults and ask them if auto racing is their favorite sport.

a. Find the probability that At most 40 say auto racing is their favorite

b. More than 50 say auto racing is their favorite sport

2. In a sample of 1000 adults, 150 said they are very confident in the nutritional information on restaurant menus. Three adults are selected at random without replacement.

a. Find the probability that all 3 of the adults are very confident in the nutritional information on restaurant menus.

b. Find the probability that none of the 3 adults are very confident in the nutritional information on restaurant menus.  

c. Find the probability that at least 1 of the 3 adults are very confident in the nutritional information on restaurant menus.  

d. Find the probability that at most 2 out of the 3 adults are very confident in the nutritional information on restaurant menus.  

e. Are any of the events from a, b, c, d unusual? Explain.  

3. In a survey of 3110 U.S. adults, 1435 say they have started paying bills online in the last year. Construct the 95% interval for the population. Be sure to interpret your results.

4. A consumer group claims that the mean annual consumption of coffee by a person in the United States is 25 gallons. A random sample of 100 people in the United States has a mean annual coffee consumption of 22.5 gallons. Assume the population standard deviation is 4.8 gallons. At ? = 0.05, can you reject the claim? Be sure to set up your hypothesis test, solve using the p-value, and interpret your results.

Answer 1

Question 1:

The number of adults out of 400 who say their favorite sport is auto racing is modelled here as:

Approximating this to a normal distribution, we get here:

a) The required probability here is computed as:

Applying the continuity correction , we get here:

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.9414 is the required probability here.

b) The required probability here is:

P(X > 50 )

Converting this to a standard normal variable, we get:

Getting it from the standard normal tables, we get:

Therefore 0.0005 is the required probability here.