Question

The weights of adult male rhesus monkeys are normally distributed with

a mean of 17 pounds and a standard deviation of 3 pounds. What is the probability
that a randomly selected adult male rhesus monkey has a weight less than
14 pounds?

Answer 1

15.87% (2 d.p.)

Explanation:

If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:

`\boxed{X \sim\text{N}(\mu,\sigma^2)}`

Given:

• Mean μ = 17 pounds
• Standard deviation σ = 3 pounds

Therefore, if the weights of adult male rhesus monkeys are normally distributed:

`\boxed{X \sim\text{N}(17, 3^2)}`

where X is the weight of an adult male rhesus monkey.

To calculate the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds, we need to find P(X < 14).

Calculator input for "normal cumulative distribution function (cdf)":

• Lower bound: x = -100
• Upper bound: x = 14
• σ = 3
• μ = 17

⇒ P (X < 14) = 0.158655253...

⇒ P (X < 14) = 15.8655253...%

⇒ P (X < 14) = 15.87%

Therefore, the probability that a randomly selected adult male rhesus monkey has a weight less than 14 pounds is approximately 15.87% (2 d.p.).