Questions: An elevator has a placard stating that the maximum capacity is 4500 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4500 / 29=155 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 33 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 155 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 155 lb. c. What do you conclude about the safety of this elevator?

An elevator has a placard stating that the maximum capacity is 4500 lb-29 passengers. So, 29 adult male passengers can have a mean weight of up to 4500 / 29=155 pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 33 lb. a. Find the probability that 1 randomly selected adult male has a weight greater than 155 lb. b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 155 lb. c. What do you conclude about the safety of this elevator?
Transcript text: An elevator has a placard stating that the maximum capacity is $4500 \mathrm{lb}-29$ passengers. So, 29 adult male passengers can have a mean weight of up to $4500 / 29=155$ pounds. Assume that weights of males are normally distributed with a mean of 180 lb and a standard deviation of 33 lb . a. Find the probability that 1 randomly selected adult male has a weight greater than 155 lb . b. Find the probability that a sample of 29 randomly selected adult males has a mean weight greater than 155 lb . c. What do you conclude about the safety of this elevator?
failed

Solution

failed
failed

Solution Steps

Step 1: Calculating the probability for 1 randomly selected adult male

Given a maximum capacity of 4500lb for 29 passengers, each passenger's mean weight limit is 155.1724lb. Using the Z-score formula for a single observation: $Z = \frac{X - \mu}{\sigma} = \frac{155.172 - 1}{33} = -0.752.$ The probability that 1 randomly selected adult male has a weight greater than 155.1724lb is approximately 0.774.

Step 2: Calculating the probability for a sample of N randomly selected adult males

Using the Z-score formula for a sample mean: $Z = \frac{\bar{X} - \mu}{\sigma / \sqrt{N}} = \frac{155.172 - 1}{33 / \sqrt{29}} = -4.051.$ The probability that a sample of 29 randomly selected adult males has a mean weight greater than 155.1724lb is approximately 1.

Final Answer:

Based on the calculated probabilities, the elevator may not be considered safe due to a high probability of overload.

Was this solution helpful?
failed
Unhelpful
failed
Helpful

Questions asked by other users

failedAnswered
f(x, y) = x^2 e^(-x^2-y^3) 1. fy = 2 x^3 y^2 e^(-x^2-y^3) 2. fy = 2 x^2 y^3 e^(-x^2-y^3) 3. fy = -3 x^2 y^2 e^(-x^2-y^3) 4. fy = -3 x^3 y^2 e^(-x^2-y^3) 5. fy = 3 x^2 y^2 e^(-x^2-y^3) 6. fy = -2 x^2 y^3 e^(-x^2-y^3)
failedAnswered
In Marissa's calculus course, attendance counts for 10% of the grade, quizzes count for 15% of the grade, exams count for 55% of the grade, and the final exam counts for 20% of the grade. Marissa had a 100% average for attendance, 89% for quizzes, 86% for exams, and 85% on the final. Determine Marissa's course average. Marissa's course average is %. (Type an integer or a decimal. Do not round.)
failedAnswered
Perform the indicated operation. Write the answer in lowest terms. x/(x+13) + 13/(x+13) Choose the correct answer below. A. (x-13)/(x+13) B. (x-13)/(13x) C. 1 D. -1
failedAnswered
Why does salt dissolve in water?
failedAnswered
Convert the following decimals to percents. 0.008=0.8 % 0.31=31.0 % 9.1=910.0 % 0.05=