Question

Historically, the average score of PGA golfers for one round is 74 with a standard deviation of 3.91. A random sample of 110 golfers is taken. What is the probability that the sample mean is between 73.63 and 74?

Question 2 options:

	1) 0.3395
	2) 0.0377
	3) 0.6605
	4) The sample mean will never fall in this range.
	5) 0.4162

Answer 1

Solution :

Given that,

mean = = 74

standard deviation = = 3.91

n = 110

= = 74

= / n = 3.91/ 110 = 0.3728

P( 73.63 < < 74)  

= P[(73.63 - 74) /0.3728 < ( - ) / < (74 -74) /0.3728 )]

= P( -0.99 < Z < 0 )

= P(Z < 0 ) - P(Z < -0.99)

= 0.5 - 0.1611 = 0.3395

probabilty = 0.3395

Answer = 1) 0.3395