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 μ = 87 and standard deviation σ = 22. 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 .8888 Correct: Your answer is correct. (b) x is less than 110 Incorrect: Your answer is incorrect. (c) x is between 60 and 110 (d) x is greater than 125 (borderline diabetes starts at 125)

Answer 1

Solution :

Given that ,

mean = = 87

standard deviation = = 22

(b)

P(x < 110) = P((x - ) / < (110 - 87) / 22)

= P(z < 1.05)

= 0.8531

Probability = 0.8531

(c)

P(60 < x < 110) = P((60 - 87)/ 22) < (x - ) /  < (110 - 87) / 22) )

= P(-1.23 < z < 1.05)

= P(z < 1.05) - P(z < -1.23)

= 0.8531 - 0.1093

= 0.7438

Probability = 0.7438

(d)

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

= 1 - P((x - ) / < (125 - 87) / 22)

= 1 - P(z < 1.73)

= 1 - 0.9582

= 0.0418

Probability = 0.0418