Acme Electronics makes calculators. Consumer satisfaction is one the top priorities of the company’s management. The company guarantees a refund or a replacement for any calculator that malfunctions within 2 years from the date of purchase. It is known from past data that despite all efforts, 5% of the calculators manufactured by Acme Electronics malfunction within a 2-year period. The company mailed a package of 10 randomly selected calculators to a store.

a. Let x denote the number of calculators in this package of 10 than will be returned for a refund or replacement within a 2-year period. Write the probability distribution for x.

b. Find the probability that at least 2 calculators will be returned or replaced.

c. Find the probability that no calculators will be returned or replaced.

d. Determine the mean and standard deviation of x.

a couple intends to have three children. assume (for some reason) that having a boy or a girl are not equally likely events, and that p(boy)=.4 and p(girl)=.6 for each delivery also assume the births are independent of each other

(a. what is the sample space of this experiment? Use a tree diagram and label the branches with their corresponding probabilities. Then make a table including all outcomes from the experiment with their associated probabilities.

(b. Find the probability that the couple has exactly two girls.

(C. Find the probability that the couple has at least one boy

Let X represent the discrete random variable corresponding to the number of girls the couple has. What is the probability distribution of the random variable X? Hint: Take your table above, summarize it, and list "sideways"

The American Journal of Public Health (July 1995) published a study of the relationship between passive smoking and nasal allergies in Japanese female students. The study revealed that 40% of the students from heavy-smoking families showed signs of nasal allergies on physical examination. Let x denote the number of students with nasal allergies in a random sample of 6 Japanese female students exposed daily to heavy smoking.

a. What is the probability that at least four of the students will have nasal allergies?

b. What is the probability that at least two of the students will have no nasal allergies?

c. Suppose instead of 6, a random sample of 20 Japanese female students were exposed daily to heavy smoking, what is the probability that between 4 and 14 (both points inclusive) of the students will have nasal allergies?

An urn contains six white balls and four black balls. Two balls are randomly selected from the urn. Let X represent the number of black balls selected.

(a) Identify the probability distribution of X. State the values of the parameters corresponding to this distribution.

(b) Compute P(X = 0), P(X = 1), and P(X = 2).

(c) Consider a game of chance where you randomly select two balls from the urn. You then win $2 for every black ball selected and lose $1 for every white ball selected. Let Y represent the total amount won. Represent the probability distribution of Y as a probability table.

(d) Find the mean and standard deviation of Y. Would you play this game? Explain.

2. During the 2009 tax filing season, 15.8% of all individual U.S. tax returns were prepared by H&R Block. Suppose we randomly select 3 tax returns.

(a) Describe the probability distribution for X = the number in the sample whose returns were prepared by H&R Block. In other words, for each value of x, determine the associated probability.

(b) What is the mean and standard deviation, respectively, of X?

A. 2.526; 0.399 B. 2.526; 0.632 C. 0.474; 0.399 D. 0.474; 0.632

(c) For the probability distribution modeled in this question, is the assumption that we’re sampling with or without replacement? Explain.

(d) Suppose we wanted to use the normal approximation to the binomial distribution. What are the required conditions to use this approximation and are those conditions met here? Explain.

Imagine that you are taking a very difficult test (in a statistics class of course), historically the mean grade is 43.5 out of 100 with a standard deviation of 15.2. Treating the historical average and standard deviation as parameters of a normal curve:

A.) What is the probability of passing with a score of 60 or higher.

B.) What is the probability of getting an A- (90 to 92.5)

C.) If a new class of 35 students takes the test, how many students in the new class would you expect to get a B (80 to 89) ?

D.) Given your results assume that we actually gave such a test to 10 sections (of ten students each) and discovered that the average number of students getting an A on the exam in each section was 7. Using your knowledge of probability what can you suggest about this situation ?

1. 5 People are attending a concert and have reserved 5 seats all in the same row. Persons 1 & 2 are a couple and want to sit together. How many ways can these people arrange themselves in the seats?

   1. a) Using this information and Excel, create a table that depicts all possible arrangements of the seats.

   2. b) Create a probability model to calculate the number of arrangements using Excel function. Hints: In creating your probability model, you will use the Product Rule and Permutations counting rules. There are more than 40 and less than 75 arrangements.

   For 1 bonus point, calculate the probability that person 1 and 3 are seated next to each other using Excel’s Count functions and your table. Still assume that Persons 1 & 2 are sitting next to each other.

The average price of a television on a certain Web site is ​$840. Assume the price of these televisions follows the normal distribution with a standard deviation of $160.

Complete parts a through d below.

a. What is the probability that a randomly selected television from the site sells for less than ​$700?

​(Round to four decimal places as​ needed.)

b. What is the probability that a randomly selected television from the site sells for between

​$400 and ​$500?

​(Round to four decimal places as​ needed.)

c. What is the probability that a randomly selected television from the site sells for between

​$900 and ​$1,000​?

​(Round to four decimal places as​ needed.)

d. There are 13 televisions on the site. How many televisions are within a ​$800

​budget? There are nothing televisions on the site that are within a ​$800 budget.

​(Round down to the nearest whole​ number.)