The weight of an energy bar is approximately normally distributed with a mean of 42.15 grams with a standard deviation o
Posted: Mon Jul 11, 2022 11:41 am
The weight of an energy bar is approximately normallydistributed with a mean of
42.15
grams with a standard deviation of
0.035
gram. Complete parts (a) through (e) below.
Question content area bottom
Part 1
a. What is the probability that an individual energy bar weighsless than
42.125
grams?
enter your response here
(Round to three decimal places as needed.)
Part 2
b. If a sample of
4
energy bars is selected, what is the probability that thesample mean weight is less than
42.125
grams?
enter your response here
(Round to three decimal places as needed.)
Part 3
c. If a sample of
25
energy bars is selected, what is the probability that thesample mean weight is less than
42.125
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 bethought of as a sample with sample size
enter your response here.
Therefore, the standard error of the mean for an individual baris
enter your response here
times the standard error of the sample in (c) with samplesize 25. This leads to a probability in part (a) that is
▼
the same as
larger than
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 sizein (b), so the standard error of the mean (or thestandard deviation of the sampling distribution) in (c)is
▼
less
greater
than in (b). As the standard error
▼
decreases,
increases,
values become more concentrated around themean. Therefore, the probability that the sample mean willfall close to the population mean will always
▼
increase
decrease
when the sample size increases.
42.15
grams with a standard deviation of
0.035
gram. Complete parts (a) through (e) below.
Question content area bottom
Part 1
a. What is the probability that an individual energy bar weighsless than
42.125
grams?
enter your response here
(Round to three decimal places as needed.)
Part 2
b. If a sample of
4
energy bars is selected, what is the probability that thesample mean weight is less than
42.125
grams?
enter your response here
(Round to three decimal places as needed.)
Part 3
c. If a sample of
25
energy bars is selected, what is the probability that thesample mean weight is less than
42.125
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 bethought of as a sample with sample size
enter your response here.
Therefore, the standard error of the mean for an individual baris
enter your response here
times the standard error of the sample in (c) with samplesize 25. This leads to a probability in part (a) that is
▼
the same as
larger than
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 sizein (b), so the standard error of the mean (or thestandard deviation of the sampling distribution) in (c)is
▼
less
greater
than in (b). As the standard error
▼
decreases,
increases,
values become more concentrated around themean. Therefore, the probability that the sample mean willfall close to the population mean will always
▼
increase
decrease
when the sample size increases.