The weight of an energy bar is approximately normally distributed with a mean of 42.50 grams with a standard deviation of 0.025 gram. Complete parts(a) through(e) below.

a. What is the probability that an individual energy bar weighs less than 42.485 grams?

. 274

.274 (Round to three decimal places asneeded.)

b. If a sample of 4 energy bars isselected, what is the probability that the sample mean weight is less than 42.485 grams?

.115 (Round to three decimal places asneeded.)

c. If a sample of 25 energy bars isselected, what is the probability that the sample mean weight is less than 42.485 grams?

.001 (Round to three decimal places asneeded.)

d. Explain the difference in the results of(a) and(c).

Part(a) refers to an individualbar, 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 notround.)

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 samplingdistribution) in(c) is less than in(b). As the standard error decreases, values become more concentrated around the mean.Therefore, the probability that the sample mean will fall close to the population mean will always increase when the sample size increases.