part 1: Consider the following contingency table that reports the results of a sample of 50people that looks at the relationship between high and low income and whether or not a respondent has a Kaplan degree.

Has a Kaplan degree Does not have a Kaplan degree total

High income 20 7 27

low income 8 15 23

total 28 22 50

Part A

Calculate the following probabilities:

1.The probability that a person has a Kaplan degree. (1 mark)

2.The probability that a person has a Kaplan degree and is a high-income earner. (1 mark)

3.The probability that a person has a Kaplan degree or is a high-income earner. (1 mark)

4.The probability that a person is a high-income earner given they have a Kaplan degree. (1 mark)

Part B

Determine if income level and Kaplan degree are independent. (You can refer to your probability calculations in Part A.)

Part C

Consider the situation where a customer has a 20% probability of making a purchase when entering a shop.If six customers enter the shop, calculate the probability of exactly three customers making a purchaseusing:

1.The binomial formula. (2 marks)

2.The cumulative binomial table. (2 marks)

Calculate the mean and variance of this distribution.