Statistics and Probability Answers

Compute the estimate of the y−intercept b0 of the regression equation.

A trucking firm suspects the claim that the average lifetime of

certain tires is 28, 000 miles. To check the claim, the firm puts 40

of these tires on its trucks and gets a mean lifetime of 27, 463

miles with a standard deviation of 1, 348 miles. Can we accept the

claim at the significance level = 0.01 (i.e. the type I error is to

be at most 0.01) using rejection region

A takeaway pizza shop conducted analysis of the takeaway meals ordered, and found that 40%

of orders were for a meat pizza with a drink, 20% for a vegetarian pizza with a drink, 10% for a

meat pizza without a drink, and 30% for a vegetarian pizza without a drink. If a takeaway order is

randomly selected, find the probability that it is for:

(a) A meat pizza without a drink. (2)

(b) An order with a drink. (2)

(c) A meat pizza. (2)

(d) A meat pizza or an order with a drink. (3)

(e) A meat pizza, if the order included a drink. (2)

(f) An order with a drink, if a vegetarian pizza was ordered.

Assume that a weather forecast for tomorrow states that it rains in Johannesburg with probability

0.2, and it rains in Pretoria with probability 0.3. Assume further that we are told that if it does rain

in Pretoria, then it rains in Johannesburg with probability 0.8. Calculate the following:

(a) The probability that it rains in both Pretoria and Johannesburg. (4)

(b) The probability that it rains in at least one of the cities. (4)

(c) The probability that it does not rain in either city. (2)

(d) The probability that it rains in Pretoria, if it rains in Johannesburg

The following data describes the gender and marital status of 100 UNISA employees.

Marital Status

Gender Single Married Divorced

Male 25 15 5

Female 30 20 5

Suppose that an employee is selected at random.

(a) Construct the joint and marginal probability table. (6)

(b) Find the probability that the employee selected is a married male. (2)

(c) Find the probability that the employee selected is married or divorced. (4)

(d) Find the probability that the employee selected is divorced given that he is male. (4)

(e) Are gender or marital status independent in this data set? Justify your answer

Students taking a module have a year mark above 75 with probability 20%, a year mark between

30 and 75 with probability 60%, and a year mark below 30 with probability 20%. A student with a

year mark above 75 passes the exam with probability 70%, a student with a year mark between 30

and 75 passes the exam with probability 65% and a student with a year mark below 30 passes the

exam with probability 15%.

(a) Construct a probability tree for the described scenario. (6)

(b) What is the probability that a randomly chosen student passes the exam? (6)

(c) If a student has a year mark below 75, what is the probability that the student passes the

exam? (4)

A finite population consists of 8 elements.

10,10,10,10,10,12,18,40

A. How many samples of size n = 2 can be drawn this population?

B. List all the possible samples and the corresponding means.

C. Construct the sampling distribution of the sample means.

If events A and B are mutually exclusive, then P.A and B/ D 0.

If A and B are independent events, then P .A and B/ D P.A/
P .B/