QuestionAn elevator has a placard stating that the maximum capacity is passengers. So, 25 adult male passengers can have a mean weight of up to pounds. Assume that weights of males are normally distributed with a mean of 188 lb and a standard deviation of 33 lb . a. Find the probability that 1 randomly selected adult male has a weight greater than 140 lb. b. Find the probability that a sample of 25 randomly selected adult males has a mean weight greater than 140 lb . c. What do you conclude about the safety of this elevator? a. The probability that 1 randomly selected adult male has a weight greater than 140 lb is (Round to four decimal places as needed.)
Studdy Solution
STEP 1
1. Weights of adult males are normally distributed with a mean () of 188 lb and a standard deviation () of 33 lb.
2. We are using the standard normal distribution (Z-distribution) to find probabilities.
STEP 2
1. Calculate the probability for one randomly selected male.
2. Calculate the probability for a sample of 25 males.
3. Conclude about the safety of the elevator.
STEP 3
Calculate the Z-score for one randomly selected male with a weight greater than 140 lb using the formula:
where , , and .
STEP 4
Use the Z-score to find the probability that a randomly selected male weighs more than 140 lb. This is:
Using standard normal distribution tables or a calculator:
Thus:
The probability that 1 randomly selected adult male has a weight greater than 140 lb is:
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