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Tt. Question Viewer nergy bar is approximately normally distributed with a mean of 42.20 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. C a. What is the probability that an individual energy bar weighs less than 42.175 grams? 0.238 (Round to three decimal places as needed.) b. If a sample of 4 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.076 (Round to three decimal places as needed.) c. If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.000 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size 1. Therefore, the standard error of the mean for an individual bar is 5 times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is larger than the probability in part (c). (Type integers or decimals. Do not round.) e. Explain the difference in the results of (b) and (c). The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is ▼values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always sample size increases. error ▼than in (b). As the standard ▼when the

Tt. Question Viewer nergy bar is approximately normally distributed with a mean of 42.20 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. C a. What is the probability that an individual energy bar weighs less than 42.175 grams? 0.238 (Round to three decimal places as needed.) b. If a sample of 4 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.076 (Round to three decimal places as needed.) c. If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.000 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size 1. Therefore, the standard error of the mean for an individual bar is 5 times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is larger than the probability in part (c). (Type integers or decimals. Do not round.) e. Explain the difference in the results of (b) and (c). The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is ▼values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always sample size increases. error ▼than in (b). As the standard ▼when the

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Tt. Question Viewer nergy bar is approximately normally distributed with a mean of 42.20 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. C a. What is the probability that an individual energy bar weighs less than 42.175 grams? 0.238 (Round to three decimal places as needed.) b. If a sample of 4 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.076 (Round to three decimal places as needed.) c. If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.000 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size 1. Therefore, the standard error of the mean for an individual bar is 5 times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is larger than the probability in part (c). (Type integers or decimals. Do not round.) e. Explain the difference in the results of (b) and (c). The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is ▼values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always sample size increases. error ▼than in (b). As the standard ▼when the
Transcribed Image Text:Tt. Question Viewer nergy bar is approximately normally distributed with a mean of 42.20 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. C a. What is the probability that an individual energy bar weighs less than 42.175 grams? 0.238 (Round to three decimal places as needed.) b. If a sample of 4 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.076 (Round to three decimal places as needed.) c. If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.175 grams? 0.000 (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bar, which can be thought of as a sample with sample size 1. Therefore, the standard error of the mean for an individual bar is 5 times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is larger than the probability in part (c). (Type integers or decimals. Do not round.) e. Explain the difference in the results of (b) and (c). The sample size in (c) is greater than the sample size in (b), so the standard error of the mean (or the standard deviation of the sampling distribution) in (c) is ▼values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always sample size increases. error ▼than in (b). As the standard ▼when the
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