Question

Type the correct answer in each box. Use numerals instead of words. If necessary, use / for the fraction bar(s).

The weights of 1,000 men in a certain town follow a normal distribution with a mean of 150 pounds and

ndard deviation of 15 pounds.

the number of men weighing

From the data, we can conclude that the number of men weighing more than 165 pounds is

less than 135 pounds is about

Answer 1

Answer:

Approximately, 159 men weighs more than 165 pounds and  159 men weighs less than 135 pounds.

Step-by-step explanation:

We are given the following information in the question:

Mean, μ = 150 pounds

Standard Deviation, σ = 15

We are given that the distribution of weights of 1000 men is a bell shaped distribution that is a normal distribution.

Formula:

$z_{score} = \displaystyle\frac{x-\mu}{\sigma}$

P( men weighing more than 165 pounds)

P(x > 165)

$P( x > 165) = P( z > \displaystyle\frac{165 - 150}{15}) = P(z > 1)$

$= 1 - P(z \leq 1)$

Calculation the value from standard normal z table, we have,  

$P(x > 165) = 1 - 0.8413 = 0.1587 = 15.87\%$

Approximately, 159 men weighs more than 165 pounds.

P(men weighing less than 135 pounds)

P(x < 135)

$P( x < 135) = P( z < \displaystyle\frac{135 - 150}{15}) = P(z < -1)$

Calculation the value from standard normal z table, we have,  

$P(x < 135) = 0.1587 = 15.87\%$

Approximately, 159 men weighs less than 135 pounds.