Let x be a random variable that represents the level of glucose in the blood (mi

Question

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean = 85 and estimated standard deviation = 50. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)

(b) What is the probability that x < 40? (Round your answer to four decimal places.)

(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)

(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)

Explanation / Answer

for partt A and b seems same ; please clarify:

a and b) P(X<40) =P(Z<(40-85)/50)=P(Z<-0.9)=0.1841

c)

for n=3 ; std error of mean =std deviaiton/(n)1/2 =50/(3)1/2 =28.8675

hence probability =P(X<40) =P(Z<(40-85)/28.8675)=P(Z<-1.5588)=0.0595

d)

for n=5 ; std error of mean =std deviaiton/(n)1/2 =50/(5)1/2 =22.3607

hence probability =P(X<40) =P(Z<(40-85)/22.3607)=P(Z<-2.0125)=0.0221

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