Answer:
15.87% (2 d.p.)
Step-by-step explanation:
If a continuous random variable X is normally distributed with mean μ and variance σ², it is written as:
[tex]\boxed{X \sim\text{N}(\mu,\sigma^2)}[/tex]
Given:
- Mean μ = 17 pounds
- Standard deviation σ = 3 pounds
Therefore, if the weights of adult male rhesus monkeys are normally distributed:
[tex]\boxed{X \sim\text{N}(17, 3^2)}[/tex]
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.).
