Question

A school states that average tuition of their training program for various certifications taught there is $995 with a standard deviation of $100. You are not sure which course to take and just decided to enroll in a certificate course at random.

What is the probability that the tuition for the course is between $900 and $1050?

You plan to register for 9 certifications. What is the probability that the average price of certifications is between $900 and $1050?

Answer 1

Solution :

Given that ,

mean = = 995

standard deviation = = 100

(a)

P(900 < x < 1050) = P[(900 - 995)/ 100) < (x - ) /  < (1050 - 995) / 100) ]

= P(-0.95 < z < 0.55)

= P(z < 0.55) - P(z < -0.95)

= 0.7088 - 0.1711

= 0.5377

(b)

= / n = 100 / 9 = 33.3333

= P[(900 - 995) / 33.3333 < ( - ) / < (1050 - 995) / 33.3333)]

= P(-2.85 < Z < 1.65)

= P(Z < 1.65) - P(Z < -2.85)

= 0.9505 - 0.0022

= 0.9483