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Chapter 6: 6.14 (page 260)
Explain in your words why a density curve has two properties listed in Key Fact 6.1 on page 252
Density curve depicts continuous outcomes probability. As probability > 0, so the curve lies on or above horizontal axis. As total probability = 1, so total area under the curve = 1
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State the two basic properties of every density curve.
Water Taxi SafetyWhen a water taxi sank in Baltimore鈥檚 Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lb. It was also noted that the mean weight of a passenger was assumed to be 140 lb. Assume a 鈥渨orst-case鈥� scenario in which all of
the passengers are adult men. Assume that weights of men are normally distributed with a mean of 188.6 lb and a standard deviation of 38.9 lb (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).
a. If one man is randomly selected, find the probability that he weighs less than 174 lb (the new value suggested by the National Transportation and Safety Board).
b. With a load limit of 3500 lb, how many male passengers are allowed if we assume a mean weight of 140 lb?
c. With a load limit of 3500 lb, how many male passengers are allowed if we assume the updated mean weight of 188.6 lb?
d. Why is it necessary to periodically review and revise the number of passengers that are allowed to board?
Using the Central Limit Theorem. In Exercises 5鈥�8, assume that females have pulse rates that are normally distributed with a mean of 74.0 beats per minute and a standard deviation of 12.5 beats per minute (based on Data Set 1 鈥淏ody Data鈥� in Appendix B).
a. If 1 adult female is randomly selected, find the probability that her pulse rate is between 72 beats per minute and 76 beats per minute.
b. If 4 adult females are randomly selected, find the probability that they have pulse rates with a mean between 72 beats per minute and 76 beats per minute. c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Mensa Membership in Mensa requires a score in the top 2% on a standard intelligence test. The Wechsler IQ test is designed for a mean of 100 and a standard deviation of 15, and scores are normally distributed.
a. Find the minimum Wechsler IQ test score that satisfies the Mensa requirement.
b. If 4 randomly selected adults take the Wechsler IQ test, find the probability that their mean
score is at least 131.
c. If 4 subjects take the Wechsler test and they have a mean of 132 but the individual scores are lost, can we conclude that all 4 of them are eligible for Mensa?
Basis for the Range Rule of Thumb and the Empirical Rule. In Exercises 45鈥�48, find the indicated area under the curve of the standard normal distribution; then convert it to a percentage and fill in the blank. The results form the basis for the range rule of thumb and the empirical rule introduced in Section 3-2.
About______ % of the area is between z = -1 and z = 1 (or within 1 standard deviation of the mean).
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