The weight of an energy bar is approximately normally distributed with a mean of 42.15 grams with a standard deviation o

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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.