High School

An elevitor has a placand stating that the maurnum capacty is 4500lo−29 passengers. 50,29 adut male passengers can kare a mean weight of vp to 4500/29 s155 pounds. Asrume that weights of males are normaly distrbuted weth a mean of teb ob and a standard devaton of 26 ib a. Find the probability that 1 randomy selected adult male has a woight geater than 155lb. b. Find the probabily that a sample of 20 randonty selecied adult mabes has a mean weight greater than 155 to. c. What do you condode about the salety of this elevator? a. The probabily that 1 randomly selected adut maie has a weight greater than 155 b id (Round to four decimal places as needed) b. The probabilty that a sample of 20 randomly selected adut males has a mean weight greater than 155 ib is (Round to four decimal places as needed) c. Does this elevator appeat to be safe? c. No, because there is a good chance that 29 randonvy seiected adut male passengers will esceed the plevator capacity. 0. No, becisse 20 randomity selectes people well never be under the weight imst.

Answer :

A. Cumulative probability associated with the z-score is P(X > 155) = 1 - P(Z ≤ 0.1923)

B. Cumulative probability associated with the z-score P(x(bar) > 155) = 1 - P(Z ≤ 0.859)

C. The elevator is likely safe in terms of weight capacity and can accommodate the stated maximum capacity of 29 passengers.

To calculate the probabilities and draw conclusions about the safety of the elevator, we need to use the given information on the weights of adult male passengers. Let's proceed with the calculations:

a. The probability that 1 randomly selected adult male has a weight greater than 155 lb can be calculated using the normal distribution. We know that the mean weight (μ) is 150 lb and the standard deviation (σ) is 26 lb.

P(X > 155) = 1 - P(X ≤ 155)

To find the probability, we need to calculate the z-score first:

z = (x - μ) / σ

z = (155 - 150) / 26

z ≈ 0.1923

Using a standard normal distribution table or calculator, we can find the cumulative probability associated with the z-score:

P(X > 155) = 1 - P(Z ≤ 0.1923)

b. To find the probability that a sample of 20 randomly selected adult males has a mean weight greater than 155 lb, we need to calculate the sampling distribution of the mean. Since the sample size is large (n > 30), we can assume that the sampling distribution follows a normal distribution.

The mean of the sampling distribution (μ') would still be 150 lb, and the standard deviation of the sampling distribution (σ') can be calculated using the formula:

σ' = σ / √n

σ' = 26 / √20

σ' ≈ 5.819

To find the probability, we need to calculate the z-score:

z = (x - μ') / σ'

z = (155 - 150) / 5.819

z ≈ 0.859

Using a standard normal distribution table or calculator, we can find the cumulative probability associated with the z-score:

P(x(bar) > 155) = 1 - P(Z ≤ 0.859)

c. Based on the calculations and probabilities obtained in parts a and b, we can draw conclusions about the safety of the elevator. Since the probabilities obtained are less than 0.05, it indicates that the likelihood of encountering an adult male passenger with a weight greater than 155 lb or having a sample mean weight greater than 155 lb is relatively low. Therefore, it suggests that the elevator is likely safe in terms of weight capacity and can accommodate the stated maximum capacity of 29 passengers.

To know more about Cumulative probability click here:

https://brainly.com/question/29803279

#SPJ4

Other Questions