Question

Private nonprofit four-year colleges charge, on average, $27,730 per year in tuition and fees. The standard deviation is $7,332. Assume the distribution is normal. Let X be the cost for a randomly selected college. Round all answers to 4 decimal places where possible

b. Find the probability that a randomly selected Private nonprofit four-year college will cost less than 28,569 per year.

c. Find the 69th percentile for this distribution.

Answer 1

Solution :

Given that ,

b.

P(x < 28569) = P[(x - $\mu$ ) / $\sigma$ < (28569 - 27730) / 7332]

= P(z < 0.1144)

= 0.5455

Probability = 0.5455

c.

Using standard normal table ,

P(Z < z) = 69%

P(Z < 0.50) = 0.69

z = 0.50

Using z-score formula,

x = z * $\sigma$ + $\mu$

x =0.50 * 7332 + 27730 = 31396

69th percentile = 31396