23 35. Probability The most important function in probability and statistics is the density function for the standard normal distribution, which is the familiar bell-shaped curve. The function is f (x) = -p - x 2/2 V2 TT a. The area under this curve between x = - 1 and x = 1 represents the probability that a normal random variable is within 1 standard deviation of the mean. Find this 32 probability. b. Find the area under this curve between x = -2 and x = 2, which represents the probability that a normal random variable is within 2 standard deviations of the mean. c. Find the probability that a normal random variable is within 3 standard deviations of the mean.Some statistics students estimated that the amount of change daytime statistics students carry is exponentially distributed with a mean of so.72. Suppose that we randomly pick 25 daytime statistics students. Part () part (b) Give the distribution of X. X-Of part (c) part (d) Give the distribution of & (Round your standard deviation to three decimal places.) part (t) Find the probability that an individual had between $0.80 and $1.00. (Found your answer to four decimal places.) Graph the situation, and shade in the area to be determined. 14 Lot 05 20 part (0) Find the probability that the average of the 25 students was between $0.80 and $1.00. [Round your answer to four decimal places.) Graph the situation, and shade in the area to be determined.P(Senior) = 22% P(Statistics Class) = 7% P(Senior and Statistics class) = 4% 4. What is the probability that a student is a Senior, but not in Statistics class? 5. What is the probability that a student will be a Senior or in Statistics class? 5. Given that a student is in a Statistics class, what is the probability that he is also a Senior