Suppose the people living in a city have a mean score of
41
and a standard deviation of
3
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
44,
(c) above
35,
(d) above
38,
(e) below
41,
(f) below
44,
(g) below
35,
and (h) below
38?
Answer)
When the scores are normally distributed
Then,
According to the emperical rule
If the data is normally distributed
Then 68% lies in between mean - s.d and mean + s.d
95% lies in between mean - 2*s.d and mean + 2*s.d
99.7% lies in between mean - 3*s.d and mean + 3*s.d
Given mean = 41
S.d = 3
Note: normal distribution is symmetrical in nature that is equal data lies on both sides of mean
A)
above 41 = 50%
B)
Above 44
44 is one s.d above the mean
That is in between 38 and 44
68% lies
So, above 44 = (100-68)/2 = 16% lies
C)
above 35
35 = mean - 2*s.d
47 = mean + 2*s.d
So 95% lies in between 35 and 47
So, above 35 = 95 + (5/2) = 97.5% lies
D)
above 38 = 68 + (32/2) = 84%
E)
Below 41 = 50%
F)
Below 44 = 68 + 16 = 84% (same logic used in part D)
G)
Below 35 = 2.5% {as above 35 = 97.5% so below 35 = 100 - 97.5)
H)
Below 38 = 16% { above 38 = 84%, so below 38 = 100-84)
Suppose the people living in a city have a mean score of 41 and a standard...
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