1. The mean of a normal distribution is 408 pounds. The standard deviation is 13 pounds. What is the area between 424 pounds and the mean of 408 pounds?
a) 0.3908
b) 0.1954
c) 0.2736
d) 0.7816
2. What is the percentage of the total area under the normal curve within plus and minus 1.6 standard deviations of the mean?
a) 29.68%
b) 17.81%
c) 89.04%
d) 44.52%
3. The mean amount spent by a family of four on food per month is $501 with a standard deviation of $73. Assuming that the food costs are normally distributed, what is the probability that a family spends less than $418 per month?
a) 0.2556
b) 0.3834
c) 0.1278
d) 0.8722
4. An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 88 minutes with a standard deviation of 142 minutes. What is the probability that the mean completion time is between 1 and 2 hours, i.e., 63 and 115 minutes?
a) 0.9322
b) 0.9714
c) About 1
d) 0.4857
5. The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 106 and a standard deviation of 14. What is the probability that a person would score 132 or more on the test?
a) 0.9684
b) 0.4684
c) 0.9484
d) 0.0316