Question

Tommy Teacher wants to analyze the weights of the students at his school. He knows the weight of the students is normally distributed so he can use the standard normal distribution. He measures the weight of 100 randomly selected students in the school. He finds the mean is 80 pounds and the standard deviation is 8 pounds.

Out of 100 students, how many should weigh between 64 and 96 pounds?

68
48
95

Answer 1

There doesn't seem to be enough information to know this question unless it wants you to estimate. So I'll estimate. the mean is basically the middle of all the numbers, with it being as high as 80 which is very close to 96, I'd say the answer is either 68 or 95.

I really don't think there's enough info to answer this question. You'd need the lowest weight of all students, and the highest weight out of all the students. I'm sorry I couldn't give you an exact answer but I hope this helps.

Answer 2

Answer: 95

Explanation:

Let x be the random variable that represents the weight of the students.

Given :
`\mu=80` and
`\sigma=8`.

Using formula :
`z=(x-\mu)/(\sigma)`

Also, the weight of the students is normally distributed.

Z-score corresponds to x= 64

`z=(64-80)/(8)=-2`

Z-score corresponds to x= 96

`z=(96-80)/(8)=2`

The probability that the students weigh between 64 and 96 pounds:

`P(64<x<96)=P(-2<z<2)\\\\=1-2P(z>|2|)\\\\=1-2(0.0227501)` [using z-table for right tailed test]

`=0.9544998\approx0.95`

Out of 100 students, the number of students weigh between 64 and 96 pounds :

`100*0.95=95`

Hence, the umber of students weigh between 64 and 96 pounds =95