Question

17) Blood glucose levels in humans have a mean value, ?, of 80 and standard deviation, ?, of 10. The blood glucose levels of 35 random patients in a very large, metropolitan hospital are found. (Give 4 decimal places where appropriate.) a. Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific. b. Describe the sampling distribution (shape, center, spread) of the sample mean blood glucose level for the 35 patients. Use symbols where appropriate. c. Find the probability that the mean for the random sample is between 78 and 81. d. Suppose that the 35 random patients have a mean glucose level above 85, which is unusual with a probability of 0.0101. Give three different explanations for this result.

          17) Blood glucose levels in humans have a mean value, ?, of 80 and standard deviation, ?, of 10. The blood glucose levels of 35 random patients in a very large, metropolitan hospital are found. (Give 4 decimal places where appropriate.)

a. Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific.

b. Describe the sampling distribution (shape, center, spread) of the sample mean blood glucose level for the 35 patients. Use symbols where appropriate.

c. Find the probability that the mean for the random sample is between 78 and 81.

d. Suppose that the 35 random patients have a mean glucose level above 85, which is unusual with a probability of 0.0101. Give three different explanations for this result.

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17) Blood glucose levels in humans have a mean value, ?, of 80 and standard deviation, ?, of 10. The blood glucose levels of 35 random patients in a very large, metropolitan hospital are found. (Give 4 decimal places where appropriate.)

a. Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific.

b. Describe the sampling distribution (shape, center, spread) of the sample mean blood glucose level for the 35 patients. Use symbols where appropriate.

c. Find the probability that the mean for the random sample is between 78 and 81.

d. Suppose that the 35 random patients have a mean glucose level above 85, which is unusual with a probability of 0.0101. Give three different explanations for this result.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert Danielle Fairburn

08/23/2023

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Verify that the three conditions for the Central Limit Theorem for means are met: a) Randomness: The problem states that the blood glucose levels are from 35 random patients, so this condition is met. b) Independence: Since the patients are from a very large Show more…

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17) Blood glucose levels in humans have a mean value, μ, of 80 and standard deviation, σ, of 10. The blood glucose levels of 35 random patients in a very large, metropolitan hospital are found. (Give 4 decimal places where appropriate.) a. Verify that the three conditions for the Central Limit Theorem for means are met. Give explanations, and be specific. b. Describe the sampling distribution (shape, center, spread) of the sample mean blood glucose level for the 35 patients. Use symbols where appropriate. c. Find the probability that the mean for the random sample is between 78 and 81. d. Suppose that the 35 random patients have a mean glucose level above 85, which is unusual with a probability of 0.0101. Give three different explanations for this result.

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Transcript

00:01 So we have blood glucose levels, which we'll call x, which have a mean value of 80 and a standard deviation of 10.

00:13 And then we're given the sample of 35 random patients in a very large hospital.

00:21 Then our x bar will be approximately normal with mean for x bar equal to the population mean and the standard deviation for x bar is going to be the population standard deviation divided by the square root of n.

00:40 So this is going to be 10 divided by the square root of 35.

00:44 And 10 divided by the square root of 35 is equal to 1 .69.

00:53 And then for port a, are the central limit theorem conditions met? yeah, we have a random sample.

01:02 So, we have a sample that is less than 0 .05 of the number of people in the hospital.

01:25 So those two are necessary for independence between our x's.

01:30 And our n is greater than or equal to 30, which means that the average approaches the normal distribution.

01:47 So we want independence or we want a random sample.

01:59 We want a sample that is smaller than 5 % of the population size and we want at least 30 in our sample.

02:09 So yes, conditions are met.

02:18 And then for part b, describe the sampling distribution.

02:22 Well, i already did that.

02:24 X will be approximately normal with mean for x bar equal to 80 and the standard deviation for x bar equal to 1 .69.

02:37 So it's bell shaped.

02:44 This is your center.

02:45 This is your spread...

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