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Weights of Water Taxi Passengers

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When a water taxi sank in the Baltimore Inner Harbor, an investigation revealed that the safe passenger load for the water taxi was 3500 lbs. It was also noted that the mean weight of a passenger was assumed to be 140 lbs. Assume a "worst case" scenario in which all 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 the weight of men are normally distributed with a mean of 172 lbs and a standard deviation of 29 lbs. Can you help me with the following questions?

a) If one man is randomly selected, what is the probability that he weighs less than 174 lbs (the new value suggested by the National Transportation and Safety Board)?
b) With a load limit of 3500 lb, how many men passengers are allowed if we assume a mean weight of 140 lbs?
c) With a load limit of 3500 lb, how many men passengers are allowed if we use the new mean weight of 174 lbs?
d) Why is it necessary to periodically review and revise the number of passengers that are allowed to board?

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Solution Summary

The weights of water taxi passengers are determined.

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a) Solution: Let X be the weight of a randomly selected man. Then X follows a normal distribution with mean of 172 lbs and a standard deviation of 29 lbs. Set Z=(X-172)/29. So, Z follows N(0, 1), the standard normal distribution. Hence, the probability that he weighs less than 174 lbs is

P(X<174)=P((X-172)/29<2/29)
=P(Z<2/29)
=P(Z<0.06897)
=0.5275

b) ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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