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Probability and Statistics Questions

Problem 1

1. (A) The number of laptops sold daily at a local electronics shop has the following probability distribution. (10 marks)

 X: # 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 agiven day?

What is the variance of the number of laptops sold on agiven day?

(B) Internet service providers (ISP) need to resolve customer problems as quickly as possible. The probability for a customer call regarding Internet service interruption is resolved within one hour is 70%. During one day, the company had 10 customer calls. (10 marks)

What is the probability that exactly fourof the customers had their problems solved? (Round your answer to the nearest thousandth).

What is the mean of the number of calls who had their problems solved?

What is the variance of the number of calls who had their problems solved?

2. Suppose a researcher goes to a small college of 200 faculty, 12 of which have blood type O-negative. He obtains a simple random sample of n = 20 of the faculty. Let the random variable X represent the number of faculty in the sample of size that have blood type O-negative.

(a) What is the probability that 3 of the faculty have blood type O-negative? (Round your answer to the nearest thousandth). (10 marks)

(b)  What is the probability that a none (x = 0) of the faculty has blood type O-negative? (Round your answer to the nearest thousandth). (5 marks)

3. (A) The replacement times for DVD players are normally distributed with a mean of 7.1 years and a standard deviation of 1.5 years (data from Consumer Reports). What is the probability that a randomly selected DVD player will be replaced in less than 5 years?  (12 marks)

(B) In a city, it is estimated that the maximum temperature in June is normally distributed with a mean of 23º and a standard deviation of 5°. Calculate the probability of having a maximum temperature between 20° and 28° (13 marks)

4. (A) Suppose the average height of men football players follows a normal distribution with a mean of 175 cm and a standard deviation of 20 cm. If a sample of 10 players is selected at random, what is the probability that the sample mean is above 185 cm?

(B) A machine fills small boxes with cereal.  The amount deposited into the box is normally distributed with a mean of 24.8 ounces and a standard deviation of 0.20 ounces.  If a sample of 9 boxes is chosen at random, what is the probability that the sample mean is between 24.9 and 25 ounces?

5. (A) In a sample of 12 men the quantity of hemoglobin in the blood stream had a mean of 15 g/dl and a standard deviation of 3 g/dl. Find the 99% confidence interval for the population mean blood hemoglobin. (Round your final answers to the nearest hundredth)

(B) A financial officer for a company wants to estimate the percent of accounts receivable that are overdue. He surveys 500 accounts and finds that 350 are overdue. Find a 95% confidence interval for the proportion of all accounts receivable that are overdue. (Round your final answers to the nearest hundredth)

(C) Interpret the results (the intervals) you got in both the scenario given above (A and B)