Question

1 on the horizontal axis witnoul & igit plu Daily activity. It appears that people who are mildly obese are less active than leaner people. One study looked at the average number of minutes per day that people spend standing or walking10 Among mildly obese people, minutes of activity varied according to the N(373, 67) distribution. Minutes of activity for lean people had the N(526, 107) distribution. Within what limits do the active minutes for about 95% of the ple in each group fall? Use the 68-95-99.7 rule. peo-

Answer 1

The 68–95–99.7 rule, also known as the empirical rule, is a shorthand used to remember the percentage of values that lie within a band around the mean in a normal distribution with a width of two, four and six standard deviations, 68.27%, 95.45% and 99.73% of the values lie within one, two and three standard deviations of the mean, respectively

95% value lie within the 2 sigma limits i.e.

$\fn_cm P(\mu -2\sigma \leq X\leq \mu -2\sigma ) \approx 0.95$

So, for obese people, the minutes of activity follow N(373,67),  the limits within which active minutes for about 95% of people fall are:

Lower limit : $\fn_cm \mu -2\sigma$ = 373 -2*67 = 239
Upper limit : $\fn_cm \mu +2\sigma$ =373 +2*67 = 507
For obese people, active minutes for about 95% of people fall in limits (239,507)

For lean people, the minutes of activity follow N(526,107), the limits within which active minutes for about 95% of people fall are:

Lower limit : $\fn_cm \mu -2\sigma$ = 526 -2*107 = 312
Upper limit : $\fn_cm \mu +2\sigma$ =526 +2*107 = 740
For obese people, active minutes for about 95% of people fall in limits (312,740)