Question

Historically, the average score of PGA golfers is 67.69 with a standard deviation of 2.763. A random sample of 50 golfers is taken. What is the probability that the sample mean is between 67.57 and 67.69?

1) 0.0173

2) 0.0469

3) 0.8795

4) 0.1205

5) The sample mean will never fall in this range.

Answer 1

Solution :

Given that,

mean = = 67.69

standard deviation = = 2.763

n = 50

= 67.69

= / n = 2.763 / 50

P(67.57 < < 67.69) = P((67.57 - 67.69) /2.763/50 < ( - ) / < (67.69 - 67.69) / 2.763/?50 ))

P P(67.57 < < 67.69) = P(-0.3071 < z < 0) =

P(67.57 < < 67.69) = P(Z < 0) - P(Z < -0.3071) Using z table,

P(67.57 < < 67.69) = 0.5 - 0.3795

P(67.57 < < 67.69) = 0.1205

Probability = 0.1205

Option 4)