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?

Answer 1

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 2

how do i solve this

Answer 3

The weight 165 pounds is 1 standard deviation above the mean weight of 150 pounds. Therefore the z-score for 165 pounds is 1.0. The cumulative probability of weights less than 65 pounds can be found from a standard normal distribution table such as the one here:
http://lilt.ilstu.edu/dasacke/eco148/ztable.htm
When you have found the cumulative probability of weights less than 165 pounds multiply by 1000 to find approximately how many people weigh less than 165 pounds.
The correct choice of answer can then be found.

Answer 4

i still dont understand really though

Answer 5

@dannyyboy Do you understand how to solve it now? If not, please ask for help on what is not clear to you.

Answer 6

Have you looked at the table at the link that I posted?

Answer 7

yeah

Answer 8

z values in the table are in the left-most column. When z is 1.0 what value is in the column next to the z value of 1.0?

Answer 9

.8413

Answer 10

Correct! So now multiply 0.8413 by 1000 to find approximately how many people weigh less than 165 pounds.
What you you get?

Answer 11

841.3

Answer 12

Correct again! Now subtract 841 from 1000 to find approximately how many people weigh more than 165 pounds.

Answer 13

159

Answer 14

\[1000-841=159\]
So what is the nearest choice of answer?

Answer 15

We have found that approximately 159 people weigh more than 165 pounds.

Answer 16

160

Answer 17

Correct. So the first answer choice applies.

Answer 18

oh thanks

Answer 19

You're welcome :)