Question

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds. Which sentence most closely summarizes the data?

About 160 people weigh more than 165 pounds.

About 320 people weigh more than 165 pounds.

About 320 people weigh less than 165 pounds.

About 640 people weigh less than 165 pounds.

Answer 1

About 160 people weigh more than 165 pounds.

Explanation:

The measured weights of 1,000 men in a certain village follow a normal distribution with a mean of 150 pounds and a standard deviation of 15 pounds.

We know that,

`z=(X-\mu)/(\sigma)`

where,

X = raw score = 165

μ = mean = 150

σ = standard deviation = 15

Putting the values,

`z=(165-150)/(15)=(15)/(15)=1`

Finding the value of probability for z=1, from z score table,

`P(z<1)=0.84=84\%`

Hence, 84% of total men will weigh less than 165 pounds. So 16% of men will be more than 165 pounds, i.e

`1000* (16)/(100)=160`