Question

The NCAA estimates that the mean yearly value of a full athletic scholarship at in-state public universities is $19,000. Assume the scholarship value is normally distributed with a standard deviation of $2000.

13. For the 10% of athletic scholarships of least value, how much are they worth?

14. What percentage of athletic scholarships are valued at $22,000 or more?

15. What is the probability than an athletic scholarship chosen at random is between $17,500 and

$22,000?

Answer 1

Solution :

13.

Using standard normal table ,

P(Z < z) = 10%

P(Z < -1.28) = 0.1

z = -1.28

Using z-score formula,

x = z * +

x = -1.28 * 2000 + 19000 = 16440

16440 much are they worth

14.

P(x $22000) = 1 - P(x   22000)

= 1 - P[(x - ) / (22000 - 19000) /2000 ]

= 1 -  P(z 1.5)   

= 1 - 0.9332

= 0.0668

percentage = 6.68%

15.

P($17500 < x < $22000) = P[(17500 - 19000)/ 2000) < (x - ) /  < (22000 - 19000) / 2000) ]

= P(-0.75 < z < 1.5)

= P(z < 1.5) - P(z < -0.75)

= 0.9332 - 0.2266

= 0.7066

Probability = 0.7066