Question

In: Statistics and Probability

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

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 μ = 81 and standard deviation σ = 25. 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 125 (borderline diabetes starts at 125)

Solutions

Expert Solution

Solution :

Given that ,

mean = = 81

standard deviation = = 25

(a)

P(x > 60) = 1 - P(x < 60)

= 1 - P((x - ) / < (60 - 81) / 25)

= 1 - P(z < -0.84)

= 1 - 0.2005   

= 0.7995

Probability = 0.7995

(b)

P(x < 110) = P((x - ) / < (110 - 81) / 25)

= P(z < 1.16)

= 0.877

Probability = 0.877

(c)

P(60 < x < 110) = P((60 - 81)/ 25) < (x - ) /  < (110 - 81) / 25) )

= P(-0.84 < z < 1.16)

= P(z < 1.16) - P(z < -0.84)

= 0.877 - 0.2005

= 0.6765

Probability = 0.6765

(d)

P(x > 125) = 1 - P(x < 125)

= 1 - P((x - ) / < (125 - 81) / 25)

= 1 - P(z < 1.76)

= 1 - 0.9608   

= 0.0392

Probability = 0.0392


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