Health care issues are receiving much attention in both academic and political arenas. A sociologist recently conducted a survey of citizens over 60 years of age whose net worth is too high to qualify for government health care but who have no private health insurance. The ages of 25 uninsured senior citizens were as follows: Suppose the mean and standard deviation are 74.0 and 9.7, respectively. If we assume that the distribution of ages is bell shaped, what percentage of the respondents will be between 64.3 and 93.4 years old

P  (  64.3  ≤  X  ≤  93.4 )  =  0.8185  =  81.85 %

Step-by-step explanation:

To find the percentage up to 93.4 years old

P ( X ≤ 93.4 )  = ??

z (s)  =  (  x  -  μ ) / σ

z(s)  =   (  93.4  -  74 ) / 9.7

z(s)  =  19.4/ 9.7

z(s)  =  2

Now with  z (s) =  2  we find in the z-table  the percentage  0,9772

P ( X ≤ 93.4 )  =  0.9772    =  97.72 %

Now to find the percentage above 64.3

P ( X ≤  64.3 )

To find z₁(s)  = ( 64.3 - 74 ) / 9.7

z₁(s)  =  - 9.7/9.7

z₁(s)  =  - 1

From z table       P ( X ≤  64.3 )   =  0.1587

Then as the part of the curve up to z = 2    ( area 0.9772 contains the area below  z = -1  we need to subtract 0.9772 - 0.1587 )

Then the percentage between 64.3  and  93.4 is:

P  (  64.3  ≤  X  ≤  93.4 )  =  0.9772  -  0.1587  = 0.8185

P  (  64.3  ≤  X  ≤  93.4 )  =  0.8185  =  81.85 %