It was noted in the Chapter Problem that when a water taxi sank in Baltimore\'s
ID: 3155611 • Letter: I
Question
It was noted in the Chapter Problem that when a water taxi sank in Baltimore's 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 "worst case" scenario in which all of the passengers are adult men. (This could easily occur in a city that hosts conventions in which people of the same gender often travel in groups.) Based on data from the National Health and Nutrition Examination Survey, assume that weights of men are normally distributed with a mean of 172 lb and a standard deviation of 29 lb. 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). With a load limit of 3500 lb, how many men passengers are allowed if we assume a mean weight of 140 lb? With a load limit of 3500 lb, how many men passengers are allowed if we use the new mean weight of 174 lb? Why is it necessary to periodically review and revise the number of passengers that are allowed to board?Explanation / Answer
MEAN = 172
STANDARD DEVIATION = 29
A)
For x = 174, the z-value z = (174 - 172) / 29 = 0.068
Hence P(x < 174) = P(z < 0.068), now from the z table we will take the value of z score = 0.068
And that value will be the probability required.
= [area to the left of 0.068] = 0.5263
B) WHEN THE LIMIT = 3500
AND THE MEAN WEIGHT = 140
THE TOTAL NUMBER WHICH CAN BOARD = 3500 / 140 = 25
C) NOW THE MEAN CHANGED = 174
THE LIMIT = 3500
THE TOTAL WHICH CAN BOARD = 3500/174 = 20.11 = 20
D) IT IS NECESSARY TO REVIEW PRIORDICALLY BECAUSE THE MEAN WEIGHT IS NORMALY DISTRIBUTED AND CAN BE CHANGED TO THE SLIGHTLY HIGHER SIDE WHICH THEREFORE CAN AFFECT THE TOTAL PEOPLE WHO CAN BOARD.
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