Question

a recent study showed that the average high school basketball team score 76 points a game with a standard deviation of 8.4 points. Find the probability that a random team scores less than 64 points

Answer 1

Answer: 0.0766

Explanation:

Let x be the random team scores.

Given: Mean = 76

Standard deviation = 8.4

We assume that x follows normal distribution.

The probability that a random team scores less than 64 points = P(x<60)

`=P((x-\mu)/(\sigma)<(64-76)/(8.4))\\\\=P(z<-1.4286) \ \ \ [Z=(x-\mu)/(\sigma)]\\\\= 1-P(z<1.4286)\\\\=1-0.9234\\\\=0.0766`

Hence, the probability that a random team scores less than 64 points =0.0766