Answer :
Answer:
[tex]\mu = 165[/tex]
[tex]\sigma = 35[/tex]
We are supposed to find the probability that it is overloaded because they have a mean weight greater than 161 lb.
n = 10 males
P(X>161)
Formula : [tex]z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
[tex]z=\frac{161-165}{\frac{35}{\sqrt{10}}}[/tex]
[tex]z=-0.3614[/tex]
Refer the z table
P(z<−0.3614)=0.6406
P(x>161)=1-P(x<161)=1-P(z<−0.3614)=1-0.6406=0.3594
The probability the elevator is overloaded is 0.3594
The elevator is safe since the probability of overload is less than 0.5
Final answer:
The question is about calculating the probability that an elevator, designed for a maximum of 10 passengers with an average weight of 161 lb, would be overloaded. Using the Central Limit Theorem and z-score calculations, it is found that there's approximately an 87% likelihood that the elevator could be overloaded. Hence, the elevator may not be entirely safe.
Explanation:
The student's question is asking for the probability that the elevator is overloaded when 10 adult male passengers are onboard, assuming their weights are normally distributed with a mean of 165 lb and a standard deviation of 35 lb. We use the Central Limit Theorem for this problem, assuming the mean weight to be 165 lb and the standard deviation to be 35 lb.
In this problem, we aim to calculate the probability that the mean weight exceeds 161 lb. We can convert this into a z-score which is a standard unit in statistics. The z-score will tell us how many standard deviations the mean weight of the passengers is above or below the average weight of 165 lb.
The z-score can be calculated as (Sample mean - Population mean) / (Standard deviation / sqrt(sample size)). Plugging in our values, we find that the z-score is (161-165) / (35/√10) = -1.13.
To find the probability, we refer to a standard z-table which gives the probability of a z score being less than a particular value. For a z-score of -1.13, the probability value is 0.1292. Thus, the probability that the elevator is overloaded is 1 - 0.1292 = 0.8708 (rounded to four decimal places).
This suggests that the elevator may not be safe as there's approximately an 87% chance it could be overloaded with 10 adult males onboard.
Learn more about Central Limit Theorem and Probability here:
https://brainly.com/question/34300003
#SPJ3
