# Statistics MCQs – Sampling Distributions Part 2

21. The average daily temperature in Johannesburg during summer follows a normal distribution with a mean of 27 degrees Celsius and a standard deviation of 15 degrees Celsius. What is the probability that a randomly chosen sample of 10 summer days will have an average temperature of less than 25 degrees?

a. 0.5832

b. 0.4168

c. 0.3372

d. 0.7357

e. 0.2643

Answer: C

22. The average daily temperature in Johannesburg during summer follows a normal distribution with a mean of 27 degrees Celsius and a standard deviation of 15 degrees Celsius. What is the probability that a randomly chosen sample of 10 summer days will have an average temperature of less than 30 degrees?

a. 0.5832

b. 0.4168

c. 0.3372

d. 0.7357

e. 0.2643

Answer: D

23. The average daily temperature in Johannesburg during summer follows a normal distribution with a mean of 27 degrees Celsius and a standard deviation of 15 degrees Celsius. What is the probability that a randomly chosen sample of 10 summer days will have an average temperature of less than 24 degrees?

a. 0.5832

b. 0.4168

c. 0.3372

d. 0.7357

e. 0.2643

Answer: E

24. Given a large population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations is greater than 78 is equal to:

a. 0.0668

b. 0.4332

c. 0.9938

d. 0.1915

e. 0.3085

Answer: A

25. Given a large population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations is greater than 70 is equal to:

a. 0.0668

b. 0.4332

c. 0.9938

d. 0.1915

e. 0.3085

Answer: C

26. Given a large population with a mean of 75 and a standard deviation of 12, the probability that the mean of a sample of 36 observations is greater than 76 is equal to:

a. 0.0668

b. 0.4332

c. 0.9938

d. 0.1915

e. 0.3085

Answer: E

27. A large population has a mean of 60 and a standard deviation of 8. A sample of 50 observations is taken at random from this population. What is the probability that the sample mean will be between 57 and 62?

a. 0.9576

b. 0.9960

c. 0.2467

d. 0.3520

e. 0.0247

Answer: A

28. At a computer manufacturing company, the size of computer chips is normally distributed with a mean of 1cm and a standard deviation of 0.1cm. A random sample of 12 computer chips is taken. What is the probability that the sample mean will be between 0.99 and 1.01cm?

a. 0.27

b. 0.50

c. 0.35

d. 0.70

e. 0.13

Answer: A

29. The time until first failure of a brand of ink jet printers is normally distributed with a mean of 1500 hours and a standard deviation of 200 hours. A large company buys four such printers. What is the probability that the mean lifetime of the four printers is more than 1600 hours?

a. 0.1587

b. 0.3413

c. 0.0668

d. 0.4332

e. 0.3085

Answer: A

30. The time until first failure of a brand of ink jet printers is normally distributed with a mean of 1500 hours and a standard deviation of 200 hours. A large company buys four such printers. What is the probability that the mean lifetime of the four printers is more than 1650 hours?

a. 0.1587

b. 0.3413

c. 0.0668

d. 0.4332

e. 0.3085

Answer: C

31. The time until first failure of a brand of ink jet printers is normally distributed with a mean of 1500 hours and a standard deviation of 200 hours. A large company buys four such printers. What is the probability that the mean lifetime of the four printers is more than 1550 hours?

a. 0.1587

b. 0.3413

c. 0.0668

d. 0.4332

e. 0.3085

Answer: E

32. Assume that the time needed by a worker to perform a maintenance operation is normally distributed with a mean of 70 minutes and a standard deviation of 6 minutes. What is the probability that the average time needed by a sample of 5 workers to perform such a maintenance is between 63 minutes and 68 minutes?

a. 0.150

b. 0.479

c. 0.007

d 0.222

e. 0.348

Answer: D

33. The diameters of Ping-Pong balls manufactured at a large factory are approximately normally distributed, with a mean of 3cm and a standard deviation of 0.4cm. A random sample of 16 Ping-Pong balls was selected. What is the probability that the sample mean diameter of the Ping-Pong balls will be between 2.7 and 3.1cm?

a. 0.49

c. 0.13

c. 0.84

d. 0.82

e. 0.34

Answer: C

34. The diameters of Ping-Pong balls manufactured at a large factory are approximately normally distributed, with a mean of 3cm and a standard deviation of 0.4cm. A random sample of 16 Ping-Pong balls was selected. What is the probability that the sample mean diameter of the Ping-Pong balls will be between 2.9 and 3.2cm?

a. 0.49

c. 0.13

c. 0.84

d. 0.82

e. 0.34

Answer: D

35. Certain electric bulbs produced by a company have a mean lifetime of 1000 hours with a standard deviation of 160 hours. The bulbs are packed in boxes of 100. What is the probability that the average lifetime for a randomly selected box exceeds 1020 hours?

a. 0.3944

b. 0.1056

c. 0.3315

d. 0.1784

e. 0.7891

Answer: B

36. The mean selling price of new apartments over a year in a small town in the Karoo was R 115 000. The population standard deviation was R25 000. A random sample of 100 new apartment sales from the town was taken. What is the probability that the sample mean selling price was between R113 000 and R117 000?

a. 1.1

b. 0.5762

c. 0.0143

d. 0.1230

e. 0.0268

Answer: B

37. The mean selling price of new apartments over a year in a small town in the Karoo was R 115 000. The population standard deviation was R25 000. A random sample of 100 new apartment sales from the town was taken. What is the probability that the sample mean selling price was more than R110 000?

a. 0.9772

b. 0.5620

c. 0.0243

d. 0.8230

e. 0.7268

Answer: A

38. A manufacturing company packages peanuts for South African Airways. The average weight of individual packages is 14.0 grams with a standard deviation of 0.6 grams. For a flight of 144 passengers receiving the peanuts, what is the probability that the average weight of peanuts per pack is less than 13.9 grams?

a. 0.0197

b. 0.2040

c. 0.0228

d. 0.4803

e. 2.0500

Answer: C

39. The distribution of gold share returns in South Africa is well approximated by a normal distribution with a mean of 12% p.a and a standard deviation of 35% p.a. A random sample of five gold shares was selected. What is the probability that the mean return of these five gold shares is greater than 6%?

a. 0.648

b. 0.352

c. 0.500

d. 0.781

e. 0.483

Answer: A

40. Independent random samples of 10 observations each are drawn from two normal populations. The parameters of these populations are: μ_{1} = 280, σ_{1} = 25 and μ_{2} = 270 and σ_{2} = 30. The difference between the two sample means has a distribution which is equal to:

a. N(10, 152.5)

b. N(20, 152.5)

c. N(10, 180)

d. N(10, 185)

e. N(20, 180)

Answer: A