Given a normal distribution with u = 103 and o = 20, and given you select a sample of n = 16, complete parts (a) through (d). a. What is the probability that X is less than 90? P(X 103.8) = 0.4364 (Type an integer or decimal rounded to four decimal places as needed.) d. There is a 70% chance that X is above what value? x =[ (Type an integer or decimal rounded to two decimal places as needed.)Given a normal distribution with [1: 5i] and a: 4. and given you select a sample of n =10l]. complete parts (a) through (d). a. What is the probability that)? is less than 49'? P[)_( 50.5): 9.1056 (Type an integer or decimal rounded to tour decimal places as needed.) d. There is a 35% chance that)? is above what value? )2 : (Type an integer or decimal rounded to two decimal places as needed.) The weight of an energy bar is approximately normally distributed with a mean of 42.75 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 42.735 grams? 0.274 (Round to three decimal places as needed.) b. If a sample of 4 energy bars is selected, what is the probability that the sample mean weight is less than 42.735 grams? 0.115 (Round to three decimal places as needed.) c. If a sample of 25 energy bars is selected, what is the probability that the sample mean weight is less than 42.735 grams? 0.001 (Round to three decimal places as needed.) 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 . Therefore, the standard error of the mean for an individual bar is 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 not round.)