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The weight of an energy bar is approximately normally distributed with a mean of 42.35 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) bela a. What is the probability that an individual energy bar weighs less than 42.325 grams? (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 42.325 grams? (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 42.325 grams? (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. Therefore, the standard error of the mean for an individual bar is times the stam the probability in part (c). sample size 25. This leads to a probability in part (a) that is

The weight of an energy bar is approximately normally distributed with a mean of 42.35 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) bela a. What is the probability that an individual energy bar weighs less than 42.325 grams? (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 42.325 grams? (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 42.325 grams? (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. Therefore, the standard error of the mean for an individual bar is times the stam the probability in part (c). sample size 25. This leads to a probability in part (a) that is

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The weight of an energy bar is approximately normally distributed with a mean of 42,35 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. a. What is the probability that an individual energy bar weighs less than 42.325 grams? (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 42.325 grams? (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 42.325 grams? (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. Therefore, the standard error of the mean for an individual bar is times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is (Type integers or decimals. Do not round.) v the probability in part (c). e. Explain the difference in the results of (b) and (c) View instructor tip Help me solve this Get more help- Next 633 PM P Type here to search- 73°F 3/31/2022 27 Insert prt sc 10 144 米 esc & 24 4 @ %23 backspace 3 5. 7. 8. W R T. Y tab
Transcribed Image Text:The weight of an energy bar is approximately normally distributed with a mean of 42,35 grams with a standard deviation of 0.035 gram. Complete parts (a) through (e) below. a. What is the probability that an individual energy bar weighs less than 42.325 grams? (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 42.325 grams? (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 42.325 grams? (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. Therefore, the standard error of the mean for an individual bar is times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is (Type integers or decimals. Do not round.) v the probability in part (c). e. Explain the difference in the results of (b) and (c) View instructor tip Help me solve this Get more help- Next 633 PM P Type here to search- 73°F 3/31/2022 27 Insert prt sc 10 144 米 esc & 24 4 @ %23 backspace 3 5. 7. 8. W R T. Y tab
(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 42.325 grams? (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 Therefore, the standard error of the mean for an individual bar is times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is V 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 V than in (b). As the standard error V values become more concentrated around the mean. Therefore, the probability that the sample mean wll fall close to the population mean will always V when the sample size increases. View instructor tip Help me solve this Get more help - Next Type here to search 633 PM 73°F 3/31/2022 27 Insert delete 144 IOI esc & $ 4 @ %23 backspace 1 3. 6. 8. Q W R Y tab G K A caps lock pause P.
Transcribed Image Text:(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 42.325 grams? (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 Therefore, the standard error of the mean for an individual bar is times the standard error of the sample in (c) with sample size 25. This leads to a probability in part (a) that is V 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 V than in (b). As the standard error V values become more concentrated around the mean. Therefore, the probability that the sample mean wll fall close to the population mean will always V when the sample size increases. View instructor tip Help me solve this Get more help - Next Type here to search 633 PM 73°F 3/31/2022 27 Insert delete 144 IOI esc & $ 4 @ %23 backspace 1 3. 6. 8. Q W R Y tab G K A caps lock pause P.
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