3] Determine the following probabilities for the standard normal random variable 2: [3] (a) P{E {1.32) ; PEI:- 1.4-5) (h) Assume X is normally distributed with a mean of 1Ill| and a standard deviation of 2. Find the value ofx so that. PO: 5 x] = [1.9!]. 4] A. certain type of storage battery lasts. on average. 3.0 years with a standard deviation of 11.5 year. Assuming that battery life is normally distributed, nd the probability that a given battery will last less than 3.1 years but greater than 2.5 years. [2] 5] The following data represent the chemistry grades for a random sample of 12 freshmen at a certain college along with their scores on an intelligence test administered while they were still seniors in high school. [10] a) Construct a scatter plot. Comment about nature ofcorrelation. 1:) Compute and interpret the sample correlation coeicient {r} and coefcient of determination (r?) c] Run a simple linear regression of y against x. d) Compute R2 and interpret. ls r2 same as R3? e) Predict y for x=8