Question

Visual sequential memory and poor spellers. Holmes, Malone and redenbach (20008) found that good readers and good spellers correctly read 93.8+2.9(M+SD) words from a spelling list. On the other hand, average readers and poor spellers correctly read 84.8 + 3.0 (M+SD) words from the same spelling list. Assuming these are normally distributed, a) what percentage of participants correctly read at least 90 words in the good readers and good spellers. b) what percentage of participants correctly read at least 90 words in the average readers and poor spellers group

Answer 1

Since it is given that distributions are normally distributed so we can use z-score.

(a)

Given that

u= 93.8,0 = 2.9

The z-score for X = 90 is

X - 90 - 93.8 - = -1.31 2.9

Using z table, the percentage of participants correctly read at least 90 words in the good readers and good spellers is

P(X > 90) = 1-PCX < 90) = 1-PC:< -1.31) = 1 -0.0951 = 0.9049

Answer: 0.9049 or 90.49%

(b)

Given that

u=84.8,0 = 3.0

The z-score for X = 90 is

x - и 90 – 84.8 3.0 - = 1.73

Using z table, the percentage of participants correctly read at least 90 words in the average readers and poor spellers group is

P(X > 90) = 1 - P(X<90) = 1- P(: <1.73) = 1 -0.9582 = 0.0418

Answer: 0.0418 or 4.18%