Probability Distributions (31 problems)

What is the standard deviation for a binomial probability distribution with n = 2412 and

Sixty-five percent of men consider themselves knowledgeable football fans. If 10 men are randomly selected, find the probability that::

a) exactly 8 of them will consider themselves knowledgeable ________

b) at least 8 of them will consider themselves knowledgeable ___________

c) at most 8 of them will consider themselves knowledgeable ____________

A history professor assigns letter grades according the following scale. Scores are normally distributed with a mean of 66 and a standard deviation of 12.8. Find the numerical limits for each letter grade. Round your answers to the nearest appropriate whole number.

A: scores in the top 10%

B: scores below the top 10% and above the bottom 60%

C: scores below the top 40% and above the bottom 20%

D: scores below the top 80% and above the bottom 10%

F: scores in the bottom 10%

The probability of a reaction to a flu shot is 0.02. If the flu shot is given to 1,000 people selected at random what is the probability that. Find the

• Mean and standard deviation
• 15 or fewer people will have a reaction
• 25 or more
• Between 20 and 30 (20 and 30 included)

In a survey, 15% of Americans said they believe they'll eventually get cancer. In a random sample 80 Americans used in he survey, find these probabilities;

A) At least 6 people in the sample believe they will get cancer.

B) Fewer than 5 people in the sample believe they will get cancer.

The on-line access computer service industry is growing at an extraordinary rate. Current estimates suggest that only 45% of the home-based computers have access to on-line services. This number is expected to grow quickly over the next five years. Suppose 25 people with home-based computers were randomly and independently sampled. Find the probability that more than five but fewer than 8 currently have access to on-line services.

Whether a baseball player gets a hit in a single "at bat" follows a Binomial distribution with p = 0.4.

a.) What is the probability of at least 4 hits in 12 "at bats"?

b.) In 20 "at bats" what is the mean and standard deviation for the proportion of "at bats" that result in a hit?

30% of the general population donate their time and energy to working on community projects. If 15 people have been randomly sampled from a community and asked if they donated their time and energy to community projects. Let x be the number of them that do donate their time an energy to community projects. Find the Probability that more than 5 of the 15 do donate their time and energy to community projects.

A certain question on a test is answered correctly by 40% of the respondents. Find the probability that among the next 300 responses there will be at least 130 correct answers.

Use the binomial distribution.

a. If n = 4 and p =.10 find P{x = 3}.

b. If n=7 and p=.80 find P{x = 4}.

c. If n=10 and p=.60 find P{x>7}.

d. If n=12 and p=.45 find P [5<x<7}

The OVRTA reports that 74% of its buses are “on time”. If 200 buses are checked at random, the probability that there are more than 150 buses “on time” could be calculated by using the normal approximation to the binomial method

In Pittsburgh Pennsylvania, about 47% of the days in a year are cloudy. Find the mean, variance, and standard deviation for the number of cloudy days during the month of June. Hint: n=30 since there are 30 days in June.

Seventy five percent of married couples paid for their honeymoon themselves. You randomly select 20 married couples and ask if they paid for their honeymoon themselves. Find the probability that the number of couples who say they paid for their honeymoon themselves is:

a) Exactly ten

b) At least twelve

c) Less than twelve

For the tossing of a fair coin 100 times what is the B or bound of a confidence interval for 95%.

It has been estimated that 17.0% if mutual fund shareholders are retired persons. Assuming the population proportion to be π = 0.17, and that a simple random sample of 400 shareholders has been selected:

a) what is the expected value of p = the proportion of those in the sample who are retired?

b) what is the standard error of the sampling distribution of the proportion, p?

c) what is the probability that at least 20% of those in the sample will be retired?

d) what is the probability that between 15% and 25% of those in the sample will be retired?

According to the Bureau of Standards, 75 percent of all people have inner belly buttons, everyone else is an outer. Let the random variable x be the number of outers among 7 randomly selected persons.

Bill must sell 3 more cars this month in order to meet his quota. Tonight he has after-dinner appointments with 5 prospective customers, each of whom happens to be interested in a different car. If he has a 30% chance of success with each customer, what is the probability the he will meet his quota by tomorrow morning/ Suppose that 3 of Bill's customers were interested in the same car, and that they'll go elsewhere if it has already been sold. Would it be appropriate to use the binomial distribution under these conditions? Why or why not?

A psychic network received telephone calls last year from over 1.5 million people. To test the credibility of the psychic network, an experiment was conducted and, 5 different cards were shuffled, and 1 is chosen at random. The psychic will then try to identify which card was drawn without seeing it. Assume that the experiment was repeated 45 times and that the results of any 2 experiments are independent of one another. If we assume that the psychic is fake, find the probability that they guess at least 3 correctly.

A steel pipe casting firm has purchased steel parts from a supplier for several years and has found that 10% of the parts must be returned because they are defective. An order of 10 parts is received.

a.) What is the probability that three or fewer of these parts are defective?

b.) What is the mean and standard deviation for the number of defective parts in orders of 10?

c.) What is the probability of receiving between 1 and 4 defective parts?

An Avon representative sells products to 25% of her customers each month. If she has 50 customers, what is the probability that she makes at most 7 sales?