A person\'s blood glucose level and diabetes are closely related. Let x be a ran

Question

A person's blood glucose level and diabetes are closely related. Let x be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean Au 86 and standard deviation o 20. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a 12-hour fast, find the following probabilities. (Round your answers to four decimal places.) (a) x is more than 60 (b) x is less than 110 (c) x is between 60 and 110 (d) x is greater than 140 (borderline diabetes starts at 140)

Explanation / Answer

Given that x follows normal distribution with mean µ=86 and standard deviation =20.

a)P(X>60)=1-P(X<60)

=1-0.0968            using excel function =NORMDIST(60,86,20,TRUE)

=0.9032

d) d)P(X>140)=1-P(X<140)

=1-0.9965            using excel function =NORMDIST(140,86,20,TRUE)

=0.0035

Given that x follows normal distribution with mean µ=8.8 and standard deviation =1.9

= 0.2638

Given that x follows normal distribution with mean µ=44.6 and standard deviation =6.7

=100*0.0996 using excel function =NORMDIST(36,44.6,6.7,TRUE)

=9.96%

We get x0= 37.0532 37 using excel function =NORMINV(0.13,44.6,6.7)

Given that x follows normal distribution with mean µ=34 and standard deviation =4

=100* 0.0062

=0.62%

We get x0= 29.854330 using excel function =NORMINV(0.15,34,4)

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