2. The amount of rainfall per month in Gotham City is normally distributed with a mean of 2.75 inches and a standard deviation of 0.5 inches. You select a random sample of 16 months and compute the mean rainfall. (a) What are the values of the mean and the standard error of the mean for this sampling distribution of the mean? (b) What is the probability that the sample mean is more than 2.90 inches? (c) What is the probability that the sample mean falls between 2.63 and 2.68 inches? (d) Find a rainfall amount such that the probability that the sample mean falls above it is 95%. (e) Find two rainfall amounts symmetric about the mean such that the probability that the sample mean falls between them is 99%. (f) What is the probability that the sample mean is below 2.35 inches? (g) Why are we justified in assuming that the sampling distribution of the mean will be normally distributed in this problem? Answer question d, e, f, g please
Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.
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