nsider the standard normal random variable Z to compute each expression.     (a) P(−1.65≤Z≤0.28)    (b)  Find the z-scores that separates the middle 86% of the distribution from the area in the tails of the standard normal distribution.

Find the probability P(-0.77 < = < -0.16) using the standard normal distribution.

You are to roll a fair die n=108  times, each time observing the number of dots appearing on the top side of the die. The number of dots showing on the topside of toss i is a random variable represented by Xi, i=1,2,⋯,108. (a) Consider the distribution of the random variable Xi. Find the mean and the standard deviation of the number of dots showing on the uppermost face of a single roll of this die.μXi= ____________ Enter your answer using all the decimals you can.σXi= ____________ Enter your answer using all the decimals you can.   (b) What is the probability that the average topside on your  tosses will be somewhere between 3.4 and 3.7? Enter your answer using all the decimals you can. _____________ (c) What is the probability that the average of your  tosses is greater than 4.15? Enter your answer using all the decimals you can. ______________