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

Answer:

About 160 people weigh more than 165 pounds.

Step-by-step 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,

$z=\dfrac{X-\mu}{\sigma}$

where,

X = raw score = 165

μ = mean = 150

σ = standard deviation = 15

Putting the values,

$z=\dfrac{165-150}{15}=\dfrac{15}{15}=1$

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

$P(z$

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

$1000\times \dfrac{16}{100}=160$

Answer 2

Z = (X-Mean)/SD 
z1 = (165 - 150)/15 = +1 
z2 = (135 - 150)/15 = - 1 
According to the Empirical Rule 68-95-99.7 
Mean +/- 1SD covers 68% of the values 
100% - 68% = 32% 
The remaining 32% is equally distributed below z = - 1 and z = +1 
32%/2 = 16% 

Therefore, 

a) Number of men weighing more than 165 pounds = 16% of 1000 = 160 
b) Number of men weighing less than 135 pounds = 16% of 1000 = 160