Question

6) Define Z score and example of how it could be useful?

11. The scores on a Northwest Ohio High Schools ACT for juniors are approximately normal with mean 21.51 and standard deviation of 5.32. What are the first and third quartiles for the ACT Scores?

14) The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a __________distribution.

Answer 1

Que.6

Z score is the numerical value which measure distance of observation from mean in standard deviation units.

Que.11

For standard normal distribution first and third quartile are,

P(z < q1 ) = 0.25

P(z< -0.67) = 0.25

Hence first quartile is -0.67.

But,

First quartile of X is, Q1 = 21.51 + 5.32 (-0.67) = 17.95

Third quartile for standard normal distribution is,

P(z< q3 ) = 0.75

P(z < 0.67) = 0.75

Hence third quartile is 0.67.

Third quartile of X is , Q3 = 21.51 + 5.32 (0.67) = 25.07

Que.14

The Central Limit Theorem states that as sample size increases, the population distribution more closely approximates a normal distribution.