A new drug claims to be effective against flu 80% of the time. The drug is tested on 24 selected patients.

a)Use the Binomial distribution to find the probability that exactly 19 patients recovered from the flu?(Round your answer to the nearest thousandth).

b)What is the mean of the number of patients who recovered from the flu?

c)What is the variance of the number of patients who recovered from the flu?

( 10 + 10 = 20 Marks )

Question 2 (20 points)

A class consists of 24 boys and 18 girls. A committee of 12 students is to be selected to represent their class in a musical competition:

a)What is the probability of having exactly 2 girls in the committee? (Round your answer to the nearest thousandth).

b)What is the probability of having exactly 5 boys in the committee? (Round your answer to the nearest thousandth).

(12 .5 + 7.5 = 20 marks)

Question 3: (20 points)

(A) The amount of tea leaves in a can from a particular production line is normally distributed with (mean) 132 grams and (Standard deviation) 12 grams.

(i) What is the probability that a randomly selected can will contain less than 125 grams of tea leaves?

(ii) If a sample of 16 cans is selected, what is the probability that the sample mean of the content "tea leaves" to be more than 135 grams?

(B) In a city, it is estimated that the maximum temperature in July is normally distributed with a mean of 27 and a standard deviation of 4. Calculate the probability of having a maximum temperature between 26 and 34

(6 + 6 + 8 = 20 marks)

Question 4: (20 points)

(A) The weight of cans of vegetables is normally distributed with a mean of 1200 grams and a standard deviation of 75 grams. What is the probability that the sample mean of weight for 10 randomly selected cans is more than 1250?

(B) The age of vehicles registered in a certain European country is normally distributed with a mean of 92 months and a standard deviation of 20 months.What is the probability that the sample mean of age for a sample of 25 vehicles is between 96 and 100 months?

(10 + 10 = 20 marks)

Question 5: (20 points)

(A) A major store is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store. Sixteen credit card accounts (n=16) were randomly sampled and analyzed with the following results: (Mean = 43.5) and Standard deviation = $ 18 (SD = 18)

a)Construct a 95% confidence interval for the mean amount its credit card customers spent on their first visit to the chain's new store.

b)Interpret the results (the interval) you got.

(B) A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 250 items, 34 are defective.

a)Find the 95% confidence interval for the proportion of defectives from this production line

b)Interpret the results (the interval) you got.