TUTORIAL 3 : (PROBABILITIES)

1. How many different arrangements can be formed by using all letters of the word ANALYSIS?

2. Four men and two women are nominees for three vacancies on a school board. How many ways can these vacancies be filled with two of the male nominees and one of the female nominees?

3. A student hostel comprises 30% Part 1 students, 20% Part 2 students and 50% Part 3 students. 2%, 4% and 5% of Part 1, 2 and 3 students have their own transport. One student is selected at random,

a. Draw a tree diagram for the above information.

b. What is the probability that a Part 1 student is without transport?

c. What is the probability that a student is without transport?

d. Given that a student is without transport, what is the probability that he or she is a Part 2 student?

4. Three companies A, B and C, are competing for a contract to build a condominium. The probabilities that company A, B and C will win the contract are 0.25, 0.45 and 0.3, respectively. If company A, B and C win the contract, the probabilities that they will profit are 0.8, 0.9 and 0.7, respectively.

a. Construct a tree diagram based on the information given in the question.

b. What is the probability that the companies will make a profit?

c. If the contract is profitable, find the probability that the contract was given to company A.

TUTORIAL 4 [SAMPLING DISTRIBUTION OF SAMPLE PROPORTIONS & SAMPLING DISTRIBUTION OF THE SAMPLE MEAN]

1. The number of calories in a salad on the lunch menu is normally distributed with mean =200 and standard deviation = 5. Find the probability that the salad you select will contain:

a. More than 208 calories.

b. Between 190 and 200 calories.

2. In recent years, Condo has become a very popular residential choice in Malaysia. AMA is currently a leading developer where offering Condo residential in Malaysia. Suppose that 25% of all Malaysian in each income and lifestyle category are interested in buying Condominium as their house. A random sample of 100 Malaysian consumers in the category of interest is to be selected. What is the probability that at least 18% of those in the sample will express an interest in Condo residential?

3. The population proportion of Americans that have a gun or revolver in their home is 0.422. You randomly select 55 adults and ask them whether they have a gun or revolver in their homes. a. Is this problem about the sample mean or about the sample proportion?

4. A 95% confidence interval for the mean number of televisions per American household is (1.15, 4.20). For each of the following statements about the above confidence interval, determine if they are correct or incorrect. If they are incorrect, state why.

a. The probability that is between 1.15 and 4.20 is .95.

b. We are 95% confident that the true mean number of televisions per American household is between 1.15 and 4.20.

c. 95% of all samples should have x-bars between 1.15 and 4.20.

d. 95% of all American households have between 1.15 and 4.20 televisions.

e. Of 100 intervals calculated the same way (95%), we expect 95 of them to capture the population mean.

f. Of 100 intervals calculated the same way (95%), we expect 100 of them to capture the sample mean