Question

Suppose the height of NBA players are approximately normally distributed, with a mean of 198 cm and a standard deviation of 12 cm.

(a) What is the probability that a randomly selected NBA player is taller than 213 cm?

(b) Determine the height which 95% of NBA players exceed.

(c) What is the probability that a team of 15 randomly selected players has an average height between 195 and 200 cm?

Answer 1

Solution :

Given that ,

mean = = 198

standard deviation = = 12

(a)

P(x > 213) = 1 - P(x < 213)

= 1 - P((x - ) / < (213 - 198) / 12)

= 1 - P(z < 1.25)

= 1 - 0.8944   

= 0.1056

Probability = 0.1056

(b)

P(Z > z) = 95%

1 - P(Z < z) = 0.95

P(Z < z) = 1 - 0.95 = 0.05

P(Z < -1.645) = 0.05

z = -1.645

Using z-score formula,

x = z * +

x = -1.645 * 12 + 198 = 178.26

height = 178.26 cm

c)

n = 15

= 198

= / n = 12 / 15

P(195 < < 200) = P((195 - 198) / 12 / 15<( - ) / < (200 - 198) / 12 / 15))

= P(-0.97 < Z < 0.65)

= P(Z < 0.65) - P(Z < -0.97) Using z table,

= 0.7422 - 0.166

= 0.5762

Probability = 0.5762