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Ch. 6 - Normal Probability Distributions
Triola - Elementary Statistics 14th Edition
Triola14th EditionElementary StatisticsISBN: 9780137366446Not the one you use?Change textbook
All textbooksTriola 14th EditionCh. 6 - Normal Probability DistributionsProblem 36c
Chapter 6, Problem 36c

Water Taxi Safety 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. 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 “Body Data” in Appendix B).


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?

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Step 1: Define the problem. We need to determine the maximum number of male passengers allowed on the water taxi, given the total weight limit of 3500 lb and the updated mean weight of 188.6 lb per passenger. The weights of male passengers are normally distributed with a mean (μ) of 188.6 lb and a standard deviation (σ) of 38.9 lb.
Step 2: Calculate the total weight of n passengers. The total weight is given by the formula: Total Weight = n × Mean Weight. Here, n represents the number of passengers, and the Mean Weight is 188.6 lb.
Step 3: Set up the inequality for the weight limit. To ensure the total weight does not exceed the limit, we use the inequality: n × 188.6 ≤ 3500. Solve this inequality for n to find the maximum number of passengers allowed.
Step 4: Round down the result. Since the number of passengers must be a whole number, round down the value of n obtained from the inequality to ensure the total weight remains within the limit.
Step 5: Verify the result. Multiply the rounded value of n by the mean weight (188.6 lb) to confirm that the total weight does not exceed 3500 lb. This ensures the solution is valid and adheres to the safety guidelines.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. In this context, the weights of adult men are normally distributed, which allows us to use statistical methods to estimate probabilities and make inferences about the population based on the mean and standard deviation.
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Mean and Standard Deviation

The mean is the average of a set of values, while the standard deviation measures the amount of variation or dispersion in a set of values. In this scenario, the mean weight of adult men is 188.6 lb, and the standard deviation is 38.9 lb, which helps us understand the typical weight of passengers and how much individual weights may vary from this average.
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Load Limit Calculation

The load limit calculation involves determining how many passengers can be safely accommodated without exceeding the maximum weight capacity. Given the load limit of 3500 lb and the mean weight of 188.6 lb per male passenger, this calculation is essential to ensure safety and compliance with regulations, allowing us to find the maximum number of passengers that can be safely transported.
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Related Practice
Textbook Question

Aircraft Seat Width Engineers want to design seats in commercial aircraft so that they are wide enough to fit 99% of all adults. (Accommodating 100% of adults would require very wide seats that would be much too expensive.) Assume adults have hip widths that are normally distributed with a mean of 14.3 in. and a standard deviation of 0.9 in. (based on data from Applied Ergonomics). Find P99. That is, find the hip width for adults that separates the smallest 99% from the largest 1%.

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Textbook Question

Durations of Pregnancies The lengths of pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days.


a. In a letter to “Dear Abby,” a wife claimed to have given birth 308 days after a brief visit from her husband, who was working in another country. Find the probability of a pregnancy lasting 308 days or longer. What does the result suggest?

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Textbook Question

Water Taxi Safety 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. 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 “Body Data” 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).

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