Question

The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3. Suppose 36 golfers played the course today. Find the probability that the average score of the 36 golfers exceeded 65. Round to four decimal places.

Answer 1

Answer:

the probability that the exceeded 65 = 0.3707

The average score of the 36 golfers exceeded 65

                        = 36 X 0.3707 = 13.3452

Step-by-step explanation:

Step 1:-

The average score of all golfers for a particular course has a mean of 64 and a standard deviation of 3.

mean (μ) = 64

standard deviation (σ) =3

by using normal distribution

given (μ) = 64 and  (σ) =3

i) when x =65

$z = \frac{x-mean}{S.D} = \frac{65-64}{3} = 0.33 >0$

P( X≥ 65) = P(z≥0.33)

              = 0.5 - A(z₁)

              = 0.5 - 0.1293 (see normal table)

             = 0.3707

The average score of the 36 golfers exceeded 65

                        = 36 X 0.3707 = 13.3452