1 A sample of 500 evening students revealed that their annual incomes from employment in industry during the day were normally distributed with a mean income of $30,000 and a standard deviation of $3,000.

(i) 250 students earned more than $30,000.

(ii) 341 students earned between $27,000 and $33,000.

(iii) 239 students earned between $24,000 and $30,000.

• (i), (ii), and (iii) are all correct statements.
• (i) is a correct statement but not (ii) or (iii).
• (i) and (iii) are correct statements but not (ii).
• (i) and (ii) are correct statements but not (iii).
• (ii) and (iii) are correct statements but not (i).

2 Normally distributed observations such as a person's weight, height, or shoe size occur quite frequently in nature. Business people who are aware of this use it to their advantage. A purchasing agent for a large retailer buying 15,000 pairs of women's shoes used the normal curve to decide on the order quantities for the various sizes. If women's average shoe size is 7.5 with a standard deviation of 1.5, how many pairs should be ordered between sizes 6.5 and 9?

• 8640
• 8849
• 8664
• 8864
• 8940

3 As the sample size (n) increases, the spread in the distribution of the sample means stays the same.

(ii) If the sampling size equals the population size, the sampling error is 1.

(iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

• (i), (ii), and (iii) are all correct statements.
• (iii) is a correct statement, but not (i) or (ii).
• (i) and (iii) are correct statements but not (ii).
• (ii) and (iii) are correct statements but not (i).
• (i), (ii), and (iii) are all false statements.

4 The mean weight of trucks traveling on a particular section of I-475 is not known. A provincial highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tonnes, with a standard deviation of the sample of 4.2 tonnes. What is probability that a truck will weigh less than 14.3 tonnes?

• 0.0062
• 0.3632
• 0.1368
• 0.4938

(i) The standard error of the mean is the standard deviation of the sampling distribution of the sample means.

(ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study.

(iii) For a sampling distribution of the means, 95% of the means would be between 1.96 standard deviations.

• (i), (ii), and (iii) are all correct statements.
• (i) and (ii) are correct statements but not (iii).
• (i) and (iii) are correct statements but not (ii).
• (ii) and (iii) are correct statements but not (i).
• (i), (ii), and (iii) are all false statements.