Concept explainers
Medical: Blood Glucose 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. After a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean
What is the
(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)?
(a)
The probability that, for an adult after a 12-hour fast, x is more than 60.
Answer to Problem 25P
Solution:
The probability that x is more than 60, for an adult after a 12-hour fast is 0.8413.
Explanation of Solution
We have random variable x having a normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix:
The probability that x is more than 60, for an adult after a 12-hour fast is 0.8413.
(b)
The probability that x is less than 110, for an adult after a 12-hour fast.
Answer to Problem 25P
Solution:
The probability that x is less than 110, for an adult after a 12-hour fast is 0.8413.
Explanation of Solution
We have random variable x having a normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix:
The probability that x is less than 110, for an adult after a 12-hour fast is 0.8413.
(c)
The probability that x is between 60 and 110, for an adult after a 12-hour fast.
Answer to Problem 25P
Solution:
The probability that x is between 60 and 110, for an adult after a 12-hour fast is 0.6826.
Explanation of Solution
We have random variable x having a normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix:
The probability that x is between 60 and 110, for an adult after a 12-hour fast is 0.6826.
(d)
The probability that x is greater125, for an adult after a 12-hour fast.
Answer to Problem 25P
Solution:
The probability that x is greater 125, for an adult after a 12-hour fast is 0.0548.
Explanation of Solution
We have random variable x having a normal distribution with
By using formula for normal distribution:-
By using Table 3 from appendix:
The probability that x is greater 125, for an adult after a 12-hour fast is 0.0548.
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