Question

The amount of time an investment banker devotes to his/her job per week is normally distributed with a mean of 70 hours and a standard deviation of 6 hours.

Find the probability that the mean amount of work per week for 9 randomly selected investment bankers is more than 72 hours. (Find the nearest answer.)

	a.	0.15866
	b.	0.06681
	c.	0.11507
	d.	0.22663
	e.	0.2275

Answer 1

Solution:-

Sample mean x̄ follows a Normal Distribution with

mean = μ = 70 and standard deviation = σ / √9 = 6 / √9 = 2

Then Z = x̄ - mean / S.D = x̄ - 70 / 2 follows Standard Normal

P (x̄ > 72)= P( x̄ - 70 / 2 > 72 - 70 / 2)

         = P (z > 1)

         = P(1 – 0.8413)

         = 0.1587

SO the Answer is option (A) 0.15866