Statistics and Probability Answers

2.8 Fifty randomly selected adults who follow professional sports were asked to name their favorite professional sports league. The results are as follows where MLB = Major League Baseball, MLS = Major League Soccer, NBA = National Basketball Association, NFL = National Football League, and NHL = National Hockey League.

NFL NBA NFL MLB MLB NHL NFL NFL MLS MLB
MLB NFL MLB NBA NBA NFL NFL NFL NHL NBA
NBA NFL NHL NFL MLS NFL MLB NFL MLB NFL
NHL MLB NHL NFL NFL NFL MLB NFL NBA NFL
MLS NFL MLB NBA NFL NFL MLB NBA NFL NFL

a. Find the frequency distribution, relative frequency distribution, and percent frequency distribution for these data.

b. Construct a frequency bar chart for these data.
c. Construct a pie chart for these data.
d. Which professional sports league is most popular with these 50 adults? Which is least popular?

2.4 A multiple choice question on an exam has four possible responses—(a), (b), (c),
and (d). When 250 students take the exam, 100 give response (a), 25 give response
(b), 75 give response (c), and 50 give response (d).

a. Write out the frequency distribution, relative frequency distribution, and
percent frequency distribution for these responses.

b. Construct a bar chart for these data using frequencies.

The mean weight of chicken in a chicken dinner at a fast food restraint is 10 ounces with standard deviation of 0.5 ounces. Using the distribution of sample means, what is the probability that the average chicken weight in a sample of 100 dinners will differ from the mean by more than 0.03 ounces?

A medical test has a false positive rate of 0.2. If 9 tests are conducted, what is the chance of getting exactly 2 false positive results?

Case Study 1. Suppose that Body Mass Index (BMI) for a population of 30-60-year-old men follows a Normal distribution with mean 26, and standard deviation 4. . Please calculate the range of BMI that 95% of subjects fall within? For a randomly selected 30-60-year old man, what is the probability that he is obese (i.e. BMI ≥ 30)?

What can you say about two groups with information as follows?

Group A: o=24, s=3
Group B: o =27, s=5

The head of XYZ Rent-a-Car believes that the mean number of miles between services is 2150 miles with standard deviation 440 miles. If he is correct, what is the probability that the mean of a sample of 36 cars would be less than 2324 miles?

The mean weight of chicken in a chicken dinner at a fast food restraint is 10 ounces with standard deviation of 0.5 ounces. Using the distribution of sample means, what is the probability that the average chicken weight in a sample of 100 dinners will differ from the mean by more than 0.03 ounces?

A medical test has a false positive rate of 0.2. If 9 tests are conducted, what is the chance of getting exactly 2 false positive results?

The probability of success in an experiment is p = 0.1. If the experiment is conducted 7 times, what is the probability that 3 or less will end in success?