Practice Questions for Exam 2Math 115B, Section 17 & 29(1) A random sample of size n = 9 yields the following values:¯xn= 5.3s2= 4Calculate a 95% confidence interval from this information and explain clearly whatthe interval does for you. In particular, provide a clear explanation of the words “95%confidence”.(2) For each of the following, give a numerical answer and a justification of your answer:(a)∞R−∞x ·13√2πe−0.5(x−53)2dx(b)∞R0(x − 8)2· 0.125e−0.125xdx(c)6R214dx(d)14R−1016√2πe−0.5(x−26)2dx2(3) Y is an exponential random variable with α = 6. If S is the standardization of Y ,determine the values of a and b and then determine the probabilities.a b Probabilitya. P (S ≤ 1) P (Y ≤ b)b. P (1 ≤ S ≤ 3) P (a ≤ Y ≤ b)c. P (S > 1) P (Y > b)(4) The p.m.f. of Y , the daily demand for a particular model of notebook computer, isgiven below.y 0 1 2fY(y) 0.4 0.35 0.25(a) Find FY(y).(b) Find µY.(c) Find σY.3(5) A company that produces snack foods uses a machine to package 455-gram bags ofpretzels. However, the variability inherent in any machine causes the actual weight ofthe bags to vary. Let W be the net weight of a randomly selected bag of pretzels. ThenW is a normal random variable with mean 455 grams and standard deviation 7.2 grams.(a) Give the formula for the p.d.f of W .(b) Draw the graph of the p.d.f of W and shade the area that corresponds to theprobability that the weight of a randomly selected bag of pretzels is at most 455grams.(c) Set up, but do not evaluate, an integral that gives the probability that the weightof a randomly selected bag of pretzels is at most 454 grams.(d) Write down exactly would be needed to in order to have the Excel function NOR-MDIST compute the probability that the weight of a randomly selected bag ofpretzels is at most 454 grams.(6) Let T be the random variable giving the number of hours per week that a randomlyselected students spends on a computer. Eight observations of T are given as follows:14, 22, 5, 10, 20, 9, 10, 24(a) Find the¯t and s.(b) Estimate E(¯T ) and V (¯T