Question

Suppose the people living in a city have a mean score of

5454

and a standard deviation of

1010

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

5454​,

​(b) above

6464​,

​(c) above

3434​,

​(d) above

4444​,

​(e) below

5454​,

​(f) below

6464​,

​(g) below

3434​,

and​ (h) below

4444​?

Answer 1

I assume that

Using the

​50%minus−​34%minus−​14% means Using of emprical rule of standard deviation which states that

Hence by Empirical rule

a) P( X>5454) means percentage of area above the mean which can be easily stated as 50 % as showcased above.

b) P(X>6464) , it says that 6464 lies at 1 standard devaition above the mean hence the prcentage of area above 1 standard deviation of the mean is 16% .

c) P(X>3434), here 3434 lies at 2 statndard deviation below the mean as

3434=5454-2*1010

so, are above -2 standard deviatin can easily be seen as

97.5%.

d)since 4444 lies at 1 standard deviatin below the mean as 4444=5454-1*1010 , hence area above the value 4444 will be

84%

e) P(X<5454) since 5454 is the mean hence below 5454 the area lies is 50%.

f) Again P(X<6464) , since 6464 lies at 1 standard deviation abuve the mean hence, the area lies below it is 84%.

g) Again P(X<3434) here 3434 lies at -2 standard deviatin hence the area lies below it is 2.5%.

h) At last P(X<4444) again here 4444 lies at -1 standard deviation below the mean hence area below -1 standard deviation is

16%.