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 = 88 and standard deviation σ = 23. 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 140 (borderline diabetes starts at
140)
Solution :
Given that ,
mean = = 88
standard deviation = = 23
a)
P(x > 60) = 1 - P(x < 60)
= 1 - P((x - ) / < (60 - 88) / 23)
= 1 - P(z < -1.22)
= 1 - 0.1112 Using standard normal table.
Probability = 0.8888
b)
P(x < 110) = P((x - ) / < (110 - 88) / 23)
= P(z < 0.96)
= 0.8315 Using standard normal table,
Probability = 0.8315
c)
P(60 < x < 110) = P((60 - 88)/ 23) < (x - ) / < (110 - 88) / 23) )
= P(-1.22 < z < 0.96)
= P(z < 0.96) - P(z < -1.22)
= 0.8315 - 0.1112 Using standard normal table,
Probability = 0.7203
d)
P(x > 140) = 1 - P(x < 140)
= 1 - P((x - ) / < (140 - 88) / 23)
= 1 - P(z < 2.26)
= 1 - 0.9881 Using standard normal table.
Probability = 0.0119
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 = 86 and standard deviation σ = 26. Note: After 50 years of age, both the mean and standard deviation tend to increase. For an adult (under 50) after a...
NORMAL PROBABILITY DISTRIBUTION Medicine: 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= 85 and standard deviation= 25. Note: After 50 years of age, both the mean and standard deviation tend to increase. What is the probability that, for an...
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 = 73 and standard deviation of σ = 20. What is the probability that, for an adult after a 12-hour fast, x is more than 85?
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 = 73 and standard deviation of σ = 20. What is the probability that, for an adult after a 12-hour fast, x is more than 85? a. 0.113 b....
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 = 73 and standard deviation of σ = 20. What is the probability that, for an adult after a 12-hour fast, x is more than 85? Select one: a....
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 a 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...
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 = 76 and standard deviation of σ = 23 What is the probability that, for an adult after a 12-hour fast, x is less than 122? Round your answer...
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 1 and standard deviation of σ 21 what s the probability that, for an adult after a 12-hour fast, x is between 113 and 121? Select one a. 0.954...
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 = 81 and standard deviation of σ = 21. What is the probability that, for an adult after a 12-hour fast, x is between 113 and 121? Select one:...
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 = 87 and standard deviation of σ = 30. What is the probability that, for an adult after a 12-hour fast, x is between 96 and 138? Round your...