Question

The golf scores for a school team were normally distributed with a mean of $68$and a standard deviation of three. Find the probability that a randomly selected golfer scored less than $65$.

Short answer

The probability that a randomly selected golfer scored less than$65$is$0.1587$

Step-by-step solution

Given Information 

Given in the question that, the golf scores for a school team were normally distributed with a mean of $68$and a standard deviation of three.

We have to find the the probability that a randomly selected golfer scored less than$65$.

Explanation 

According to the given information, we obtain that any golf scores were normally distributed.

So that $X~N(68,3)$.

Therefore, we can compute the required probability as follow:

$P(x<65)=P\left(\frac{x-\mu }{\sigma }<\frac{65-\mu }{\sigma }\right)$

$=P\left(Z<\frac{65-68}{3}\right)$

$=P(Z<-1)$

$=0.1587\left\{\begin{array}{l}\text{From standard}\\ \text{normal table}\end{array}\right\}$

Hence,$P(x<65)$is$0.1587$