Question

In a normally distributed set of scores, the mean is 35 and the standard deviation is 7. Approximately what percentage of scores will fall between the scores of 28 and 42? What range scores will fall between +2 and -2 standard deviation units in this test of scores? Please show work.

Answer 1

Solution:
Given in the question
Mean = 35
Standard deviation = 7
We need to calculate
P(28<X<42) = P(X<42) - P(X<28)
Here we will use Z standard normal table
Z = (28-35)/7 = -1
Z = (42-35)/7 = 1
From Z table we found p-value
P(28<X<42) = P(X<42) - P(X<28) = 0.8413 - 0.1587 = 0.6826
So approximately 68.26% of scores fall b/w the scores 28 and 42
Solution(b)
Here Z = +/-2
So Lower bound score = Mean - Z*SD = 35 - 2*7 = 21
Upper bound score = Mean + Z*Score = 35 + 2*7 = 49