The weight of an energy bar is approximately normally distributed with a mean of 42.9042.90 grams with a standard deviation of 0.0350.035 gram. Complete parts (a) through (e) below. Question content area bottom Part 1 a. What is the probability that an individual energy bar weighs less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 2 b. If a sample of 44 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 3 c. If a sample of 2525 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 4 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 enter your response here. Therefore, the standard error of the mean for an individual bar is enter your response here 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 same as smaller than the probability in part (c). (Type integers or decimals. Do not round.) Part 5 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 ▼ less greater than in (b). As the standard error ▼ decreases, increases, values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always ▼ increase decrease when the sample size increases.
The weight of an energy bar is approximately normally distributed with a mean of 42.9042.90 grams with a standard deviation of 0.0350.035 gram. Complete parts (a) through (e) below. Question content area bottom Part 1 a. What is the probability that an individual energy bar weighs less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 2 b. If a sample of 44 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 3 c. If a sample of 2525 energy bars is selected, what is the probability that the sample mean weight is less than 42.87542.875 grams? enter your response here (Round to three decimal places as needed.) Part 4 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 enter your response here. Therefore, the standard error of the mean for an individual bar is enter your response here 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 same as smaller than the probability in part (c). (Type integers or decimals. Do not round.) Part 5 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 ▼ less greater than in (b). As the standard error ▼ decreases, increases, values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always ▼ increase decrease when the sample size increases.
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter10: Statistics
Section10.3: Measures Of Spread
Problem 3CYU
Related questions
Question
The weight of an energy bar is approximately normally distributed with a mean of
42.9042.90
grams with a standard deviation of
0.0350.035
gram. Complete parts (a) through (e) below.Question content area bottom
Part 1
a. What is the probability that an individual energy bar weighs less than
42.87542.875
grams?enter your response here
(Round to three decimal places as needed.)Part 2
b. If a sample of
44
energy bars is selected, what is the probability that the sample mean weight is less than
42.87542.875
grams?enter your response here
(Round to three decimal places as needed.)Part 3
c. If a sample of
2525
energy bars is selected, what is the probability that the sample mean weight is less than
42.87542.875
grams?enter your response here
(Round to three decimal places as needed.)Part 4
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
the probability in part (c).
enter your response here.
Therefore, the standard error of the mean for an individual bar is
enter your response here
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 same as
smaller than
(Type integers or decimals. Do not round.)
Part 5
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
than in (b). As the standard error
values become more concentrated around the mean. Therefore, the probability that the sample mean will fall close to the population mean will always
when the sample size increases.
▼
less
greater
▼
decreases,
increases,
▼
increase
decrease
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