Ergonomics. Exercises 9–16 involve applications to ergonomics, as...

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1. Intro to Stats and Collecting Data55m
2. Describing Data with Tables and Graphs1h 55m
3. Describing Data Numerically1h 45m
4. Probability2h 16m
5. Binomial Distribution & Discrete Random Variables2h 33m
6. Normal Distribution and Continuous Random Variables1h 38m
7. Sampling Distributions & Confidence Intervals: Mean1h 3m
- Introduction to Confidence Intervals
  15m
- Confidence Intervals for Population Mean
  48m
8. Sampling Distributions & Confidence Intervals: Proportion1h 12m
- Sampling Distribution of Sample Proportion
  29m
- Confidence Intervals for Population Proportion
  42m
9. Hypothesis Testing for One Sample1h 1m
- Steps in Hypothesis Testing
  1h 1m
10. Hypothesis Testing for Two Samples2h 8m
11. Correlation48m
- Scatterplots & Intro to Correlation
  26m
- Correlation Coefficient
  21m
12. Regression1h 4m
13. Chi-Square Tests & Goodness of Fit1h 20m
14. ANOVA1h 0m

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

Statistics

6. Normal Distribution and Continuous Random Variables

Standard Normal Distribution

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1:36 minutes

Problem 6.4.11a

Textbook Question

Ergonomics. Exercises 9–16 involve applications to ergonomics, as described in the Chapter Problem.

Water Taxi Safety Passengers died when a water taxi sank in Baltimore’s Inner Harbor. Men are typically heavier than women and children, so when loading a water taxi, assume a worst-case scenario in which all passengers are men. Assume that weights of men are normally distributed with a mean of 189 lb and a standard deviation of 39 lb (based on Data Set 1 “Body Data” in Appendix B). The water taxi that sank had a stated capacity of 25 passengers, and the boat was rated for a load limit of 3500 lb.

a. Given that the water taxi that sank was rated for a load limit of 3500 lb, what is the maximum mean weight of the passengers if the boat is filled to the stated capacity of 25 passengers?

Verified step by step guidance

Step 1: Understand the problem. The goal is to determine the maximum mean weight of passengers such that the total weight does not exceed the boat's load limit of 3500 lb when the boat is filled to its stated capacity of 25 passengers.

Step 2: Set up the relationship between the total weight, mean weight, and number of passengers. The total weight of the passengers can be expressed as: \( \text{Total Weight} = \text{Mean Weight} \times \text{Number of Passengers} \).

Step 3: Substitute the given values into the equation. The total weight is limited to 3500 lb, and the number of passengers is 25. This gives: \( 3500 = \text{Mean Weight} \times 25 \).

Step 4: Solve for the mean weight. Rearrange the equation to isolate the mean weight: \( \text{Mean Weight} = \frac{3500}{25} \).

Step 5: Interpret the result. The calculated mean weight represents the maximum allowable average weight per passenger to ensure the total weight does not exceed the boat's load limit of 3500 lb.

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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 men are assumed to follow a normal distribution with a specified mean and standard deviation, which allows for the calculation of probabilities and percentiles related to weight.

Mean Weight Calculation

The mean weight is the average weight of a group of individuals, calculated by summing all individual weights and dividing by the number of individuals. In this scenario, to find the maximum mean weight for 25 passengers without exceeding the load limit, one must divide the total load limit (3500 lb) by the number of passengers (25).

Load Capacity and Safety Regulations

Load capacity refers to the maximum weight a vehicle or structure can safely carry. In the case of the water taxi, understanding the load capacity is crucial for ensuring safety, as exceeding this limit can lead to dangerous situations, such as capsizing. This concept emphasizes the importance of adhering to safety regulations in transportation.

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Key Concepts

Normal Distribution

Mean Weight Calculation

Load Capacity and Safety Regulations

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