Question

If the scores per round of golfers on the PGA tour are approximately normally distributed with mean 65.5 and standard deviation 1.51, what is the probability that a randomly chosen golfer's score is between 64 and 66 strokes?

Question 9 options:

	1) We do not have enough information to calculate the value.
	2) 0.4695
	3) 0.1603
	4) 0.3703
	5) 0.0076

The daily stock price for International Business Machines (IBM) historically has followed an approximately normal distribution (when adjusting for inflation) with a mean of $138.918 and standard deviation of $2.8408 Approximately 35.53% of days IBM had a stock price less than what dollar amount?

Question 11 options:

	1) 135.92
	2) 139.97
	3) 137.86
	4) 141.91
	5) We do not have enough information to calculate the value.

Answer 1

Solution :

Given that,

mean = = 65.5

standard deviation = = 1.51

9) P (64 < x < 66 )

P ( 64 - 65.5 / 1.51) < ( x -  / ) < ( 66 - 65.5 / 1.51)

P ( -1.5 / 1.51 < z < 0.5 / 1.51)

P (-0.9934< z < 0.3311)

P ( z < 0.3311 ) - P ( z < -0.9934)

Using z table

= 0.6297 - 0.1603

= 0.4695

Probability = 0.4695

option 2 ) is correct.

11 ) Given that,

mean = = 138.918

standard deviation = = 2.8408

Using standard normal table,

P(Z < z) = 35.53%

P(Z < z) = 0.3553

P(Z < - 0.61) = 0.3553

z = - 0.371

Using z-score formula,

x = z * +

x = -0.371 * 2.8408 + 138.918

x = 137.86

option 3 ) is correct.