Health care issues are receiving much attention in both academic and political a

Question

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: 68 73 66 76 86 74 61 89 65 90 69 92 76 62 81 63 6% 81 70 73 60 87 75 64 82 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?

Explanation / Answer

We first get the z score for the two values. As z = (x - u) / s, then as          
x1 = lower bound =    64.3      
x2 = upper bound =    93.4      
u = mean =    74      
          
s = standard deviation =    9.7      
          
Thus, the two z scores are          
          
z1 = lower z score = (x1 - u)/s =    -1      
z2 = upper z score = (x2 - u) / s =    2      
          
Using table/technology, the left tailed areas between these z scores is          
          
P(z < z1) =    0.158655254      
P(z < z2) =    0.977249868      
          
Thus, the area between them, by subtracting these areas, is          
          
P(z1 < z < z2) =    0.818594 = 81.8%   

[ANSWER: A: 81.5%, CLOSEST]      

********************

Note that the difference could be due to round off error. The answer above is exact.

Related Questions

Navigate

• Browse (All)
• Browse H
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.