Question

Suppose the people living in a city have a mean score of 41 and a standard deviation of 8 on a measure of concern about the environment. Assume that these concern scores are normally distributed. Using the ​50% minus −​34% minus −​14% ​figures, approximately what percentage of people have a score​ (a) above 41​, ​(b) above 49​, ​(c) above 25​, ​(d) above 33​, ​(e) below 41​, ​(f) below 49​, ​(g) below 25​, and​ (h) below 33​?

Answer 1

• First step:-

transform the raw scores into z-scores.

• Second step

go to the unit normal table and locate your z-score.

• Third step

check back with the question, find out if you want the area to the left or right of the z-score.

a) above 41?
b) above 49?
c) above 25?
d) above 33?
e) below 41?
f) below 49?
g) below 25?

(h) below 33?

• (41-41)/8= 0, so the point is at the mean, look at the table p = .50
• (49-41)/8 = 1, so the point is one standard deviation above the mean, look at the table p = .1587
• (25-41)/8= -2, so the point is two standard deviations below the mean, look at the table p = 1.0 - 0.0228 = .9772
• (33-41)/8 = -1, so the point is one standard deviation below the mean, look at the table p = .1.0 - 0.1587 = .8413
• (41-41)/8= 0, so the point is at the mean, look at the table p = .50
• (49-41)/5 = 1, so the point is one standard deviation below the mean, look at the table p = .1587
• (25-41)/8 = 2, so the point is is two standard deviations below the mean, look at the table p = .0228
• (33-41)/8= -1, so the point is one standard deviation below the mean, look at the table p = .1587

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