I need help with a Business question. All explanations and answers will be used to help me learn.

All the questions in the file below

Question 1: (20 points)

(A) The number of laptops sold daily at a local electronics shop has the following probability distribution.

X: No. of laptops sold 12 13 14 15

P(X=x) 0.4 0.3 0.2 0.1

⦁ What is the mean of the number of laptops sold on a given day?

⦁ What is the variance of the number of laptops sold on a given day?

(B) A new drug claims to be effective against flu 70% of the time. The drug is tested on 28 selected patients.

⦁ Use Binomial distribution to find the probability that exactly 21 patients recovered from the flu? (Round your answer to the nearest thousandth).

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

⦁ 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 12 boys and 10 girls. A committee of 5 students is to be selected to represent their class in a musical competition:

⦁ What is the probability of having exactly 1 girl in the committee? (Round your answer to the nearest thousandth).

⦁ What is the probability of having exactly 3 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 μ (mean) = 110 grams and σ (Standard deviation) = 5 grams.

(i) What is the probability that a randomly selected can will contain less than 105 grams of tea leaves?

(ii) If a sample of 9 cans is selected, what is the probability that the sample mean of the content “tea leaves” to be more than 115 grams?

(B) In a city, it is estimated that the maximum temperature in July is normally distributed with a mean of 23º and a standard deviation of 4°. Calculate the probability of having a maximum temperature between 20° and 28°

(6 + 6 + 8 = 20 marks)

Question 4: (20 points)

(A) The weight of cans of vegetables is normally distributed with a mean of 1000 grams and a standard deviation of 50 grams. What is the probability that the sample mean of weight for 10 randomly selected cans is more than 1040?

(B) The age of vehicles registered in a certain European country is normally distributed with a mean of 98 months and a standard deviation of 15 months. What is the probability that the sample mean of age for a sample of 36 vehicles is between 100 and 102 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. Fifteen credit card accounts (n=15) were randomly sampled and analyzed with the following results: and S = 20.

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

⦁ 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 200 items, 28 are defective.

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

⦁ Interpret the results (the interval) you got.

(10 + 10 = 20 marks)