The amount of water in a bottle is approximately normally distributed with a mean of 2.25 liters with a standard deviation of 0.025 liter. Complete parts (a) through (e) below. (Round to three decimal places as needed.) b. If a sample of 4 bottles is selected, what is the probability that the sample mean amount contained is less than 2.23 liters? (Round to three decimal places as needed.) c. If a sample of 25 bottles is selected, what is the probability that the sample mean amount contained is less than 2.23 liters? (Round to three decimal places as needed.) d. Explain the difference in the results of (a) and (c). Part (a) refers to an individual bottle, which can be thought of as a sample with sample size 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.) e. Explain the difference in the results of (b) and (c). Therefore, the standard error of the mean for an individual bottle is the probability in part (c). times the standard 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 standard error than in (b). As the 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.