Statistics and Probability Answers

Two cards are drawn from a well shuffled pack of playing cards. Calculate the probability of the

events (i) there is one card of black suits and other of red suits, (ii) both the card are aces (iii)

both the cards are hearts 

The editor of a textbook publishing company is trying to decide whether to publish a proposed business statistics textbook. Information on previous textbooks publishes indicates that 10% are huge successes, 20% are modest successes, 40% break even and 30% are losers. However before a publishing decision is made, the book will be reviewed. In the past, 99% of the huge successes received favourable reviews, 70% of the moderate successes received favourable reviews, 40% of the break even books received favourable reviews and 20% of the losers received favourable reviews.

a) If the proposed textbooks receives a favourable review, how should the editor revise the probabilities of the various outcomes to take this information into account?

b) What proportion of textbooks receives favourable reviews?

 State the null hypothesis and the alternative hypothesis in (a) words and in 

(b) symbols for each of the following. 

a. A librarian of a school claims that all their grade 8 students read an 

average of 10 storybooks a month with a standard deviation of 2 books. 

A random sample of grade 8 students read an average 12 books a month 

and a standard deviation of 1 book. The confidence statement is 95%. 

b. According to a factory employer, the mean working time of workers in 

the factory is 6 hours with a standard deviation of 0.5 hours. A 

researcher interviewed 50% of the employees and found out that their 

mean working time is 8 hours with a standard deviation of 1 hour. The a 

level is 0.05. 

 A marketing company, Groupe RM, has developed an index that seeks to determine the audience size and composition of television programming using a rating system. In one survey, Groupe RM found that 101 out of 165 sampled people watched “Sinking Sands” on the night of its premiere. In a separate survey later in the year, Groupe RM found that 97 out of 180 sampled people watched “Adams Apple” by Sparrows Production on its premiere.

(a) Estimate the true proportion p1 of all TV-viewing people who watched the premiere of Sinking Sands and obtain a 95% confidence interval for p1.

(b) Briefly explain what this 95% confidence interval means.

(c) If the Groupe RM company wanted to guarantee that all proportions are estimated to within ±0.05 with 95% confidence, how large should their samples be?

(d) Let p2 be the true proportion of all TV-viewing families who watched the premiere of Adams Apple. Estimate p1 −p2 and obtain a 95% confidence interval for p1 −p2.

If you were to randomly survey 10 people at a 100 random eyeglasses stores across the country with this be a random sample why are why not

. A contractor on the Eastern Corridor road makes a large purchase of industrial cement from Ghacem. Each bag of this industrial cement is supposed to weigh 94 pounds. To see if he is getting his money’s worth, the contractor weighs 10 randomly selected bags and gets the following weights (in pounds):

94.1,93.4, 92.8, 93.4, 95.4, 93.5, 94.0, 93.8, 92.9, 94.2

(a) What are the appropriate null and alternative hypotheses to be tested?

(b) State the assumption that is necessary for performing the test.

(c) Calculate the p−value of the test. Perform the test at a significance level of α = 0.1. 

A psychologist believes that it will take at least an hour for certain disturbed 

children to learn a task. A random sample of 30 of these children results in a 

mean of 50 minutes to learn the task. Should the psychologist modify her belief 

at the 0.01 level if the population standard deviation can be assumed to be 15

minutes?

The number of calls received by and office every 30 minutes is a poisson random variable with a mean value of 5. Find the probability that:

a. No calls will be received in a given 30 minutes period?

b. Exactly for calls will be received in a given 30 minutes period?

An event has 50 female contestants and 13 male contestants. A random sample of 12 contestants is drawn. What is the probability that exactly it of the contestant will be female?

Random variable X arises from a binomial experiment. Use n=8 and p=60 percent when answering the following:

a. Compute for the mean

b. Compute for the variance

c. Compute for the standard deviation