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hvSIClans recommend that children with t e 1 insulin de endent diabetes keep up their Insulin shots o mininze he chance o lon erm com lications. In addition, some date es researchers have o served hat rowth rate of weight during adolescence among diabetes patients is affected by level of compliance with insulin therapy. Assume 12-year-old type-I diabetic boys who comply with their insulin shots have a weight gain over one year that is normally distributed. Using the file Type-I weights answer the following: a) What is the probability that compliant type-l diabetic 12-year-old boys will gain at least 15 lb over 1 ycar? b) What is the probability that compliant type-I diabetic 12-ycar-old boys will gain more than 15 lb over 1 ycar? c) What is the 90th percentile tor the weight gain in compliant typc-I diabctic 12-ycar-old boys?

Explanation / Answer

Solution

Let the 12 years boys weight gain over one year be X

Now, according to the data total population size, n =300 , mean = 12.06 lb and standard deviation = 4.41 lb

(a) P(X>=15) = P((X-mean)/standard dev >= (15-12.06)/4.41)

=P(Z>=0.67) = 1-P(Z<0.67) = 1- 0.74857

P(X>=15)=0.25134

(b) P(X>15) = P(Z>0.67) (from part (a))

= 1- P(Z<=0.67)

=0.25134

(c) 90th Percentile

90% of total populaton size = 0.9*300 = 270

weight on 270th number from least to highest = 17.71 lb

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