Question

A person's level of blood glucose 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 = 85 and standard deviation of σ = 26. What is the probability that, for an adult after a 12-hour fast, x is more than 46? Round your answer to the nearest thousandth.

Answer 1

after a 12-hour fast, the random variable x will have a distribution that is approximately normal with mean μ = 85 and the standard deviation of σ = 26.

What is the probability that, for an adult after a 12-hour fast, x is more than 46?

P( X > 46 ) = P( ( X - μ )/σ > ( 46 - μ )/σ )

P( X > 46 ) = P( ( X - 85 )/26 > ( 46 - 85 )/26 )

P( X > 46 ) = P( Z > -1.5 ).

P( X > 46 ) = 1 - P( Z < -1.5 )

P( X > 46 ) = 1 - 0.0668

P( X > 46 ) = 0.9332

Probability that, for an adult after a 12-hour fast, x is more than 46 is 0.933