Normal Distribution Question: If 2 men, 1 woman are randomly selected, what is prob. maximum is exceeded?

A

Audentes

Junior Member
Joined
Jun 8, 2020
Messages
187
"The weights of adult men are approximately Normally distributed with a mean of 170 pounds and a standard deviation of 30 pounds. The weights of adult women are approximately Normally distributed with a mean of 140 pounds and a standard deviation of 20 pounds.

An elevator in a small apartment building has a maximum weight capacity of 550 pounds. If two men and one woman (everyone randomly-selected of course) get on the elevator, what is the probability that they exceed the maximum capacity?"

I combined the means and SDs and got 0.068. My friends all got a different answer and the teacher marked it right.

Could someone confirm if 0.068 is the answer? Because i thought i did all the steps correctly.

thanks!
 
Audentes said:
"The weights of adult men are approximately Normally distributed with a mean of 170 pounds and a standard deviation of 30 pounds. The weights of adult women are approximately Normally distributed with a mean of 140 pounds and a standard deviation of 20 pounds.

An elevator in a small apartment building has a maximum weight capacity of 550 pounds. If two men and one woman (everyone randomly-selected of course) get on the elevator, what is the probability that they exceed the maximum capacity?"

I combined the means and SDs and got 0.068. My friends all got a different answer and the teacher marked it right.

Could someone confirm if 0.068 is the answer? Because i thought i did all the steps correctly.

thanks!
Click to expand...
I got the same answer (rounded).
 
blamocur said:
I haven't verified this, but it would be useful to post the details of your solution.
Click to expand...
Capacity = 550
Two men = 170 * 2 =340
One woman = 140
Total people weight = 480 lbs
σ = sqrt( (30)^2 + (30)^2 + (20)^2 )
σ = 10 * sqrt(22)

Casio FX-9750GII

Normal C. D
Data : Variable
Lower: -10000000
Upper: 550
σ : 10 * sqrt(22)
μ: 480
P=0.932

Complement Rule: 1-0.932=0.068

Answer: 0.068
 
Audentes said:
Capacity = 550
Two men = 170 * 2 =340
One woman = 140
Total people weight = 480 lbs
σ = sqrt( (30)^2 + (30)^2 + (20)^2 )
σ = 10 * sqrt(22)

Casio FX-9750GII

Normal C. D
Data : Variable
Lower: -10000000
Upper: 550
σ : 10 * sqrt(22)
μ: 480
P=0.932

Complement Rule: 1-0.932=0.068

Answer: 0.068
Click to expand...
Looks good to me. I get 0.6787.
 
You must log in or register to reply here.
Top