Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean u = 81 an estimated standard deviation o = 45. A test result x < 40 is an indication f severe excess insulin, and medication is usually prescribed. A USE SALT (a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.) 0.1811 (b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of X? Hint: See Theorem 6.1. ao The probability distribution of x is not normal. bo The probability distribution of x is approximately normal with = 81 and o, = 31.82. Co The probability distribution of x is approximately normal with ug = 81 and oz = 22.50. What is the probability that x < 40? (Round your answer to four decimal places.) (c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.) 0.0572 (d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.) 0.0211 (e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased? O Yes O No Explain what this might imply if you were a doctor or a nurse. a O The more tests a patient completes, the weaker is the evidence for lack of insulin. b O The more tests a patient completes, the stronger is the evidence for lack of insulin. O The more tests a patient completes, the stronger is the evidence for excess insulin.

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Description: Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 81 and

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Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean ? = 81 and estimated standard deviation ? = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.

(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.

What is the probability that x < 40? (Round your answer to four decimal places.)

Explain what this might imply if you were a doctor or a nurse. (Select one of the options in screenshot)

Let x be a random variable that represents the level of glucose in the blood (milligrams per deciliter of blood) after a 12 hour fast. Assume that for people under 50 years old, x has a distribution that is approximately normal, with mean p = 81 and
estimated standard deviation o = 45. A test result x < 40 is an indication of severe excess insulin, and medication is usually prescribed.
n USE SALT
(a) What is the probability that, on a single test, x < 40? (Round your answer to four decimal places.)
0.1811
(b) Suppose a doctor uses the average x for two tests taken about a week apart. What can we say about the probability distribution of x? Hint: See Theorem 6.1.
a o The probability distribution of x is not normal.
bo The probability distribution of x is approximately normal with µz = 81 and o, = 31.82.
C O The probability distribution of x is approximately normal with µz = 81 and o, = 22.50.
What is the probability that x < 40? (Round your answer to four decimal places.)
(c) Repeat part (b) for n = 3 tests taken a week apart. (Round your answer to four decimal places.)
0.0572
(d) Repeat part (b) for n = 5 tests taken a week apart. (Round your answer to four decimal places.)
0.0211
(e) Compare your answers to parts (a), (b), (c), and (d). Did the probabilities decrease as n increased?
O Yes
O No
Explain what this might imply if you were a doctor or a nurse.
a
O The more tests a patient completes, the weaker is the evidence for lack of insulin.
bo The more tests a patient completes, the stronger is the evidence for lack of insulin.
O The more tests a patient completes, the stronger is the evidence for excess insulin.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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