Please help me with these questions

3. A firm has two computer systems available for processing telephone orders. At any given time, system A has a 10% chance of being 'down', while system B has just a 5% chance of being 'down'. The computer systems operate independently. For a typical telephone order, determine the probability that

a. exactly one of the computer systems will be operational.

b. at least one of them is operational.

4 The average number of calories in a regular-size bagel is 240. If the standard deviation is 38 calories, find the range in which at least 75% of the data will lie.

This is the sample test which will help you

1. Find the Mean, Median and Standard Deviation of the following data: -4, 3, 0, 1, 7, 2. Mean=X=-':I:U:"-4 3 231 7 2=15 Median: Writing in order: (- 4), 0, 1 2, 3, 7 => the number In the middle is 1+2 1.5 Standard Deviation s =\\/E_ X2 \"EXXZ =\\/((_4)2+32+02+:72+22) ixm = 3.62 2. For a statistics class of 45 students, the mean and standard deviation for the midterm score is 75 and 8 respectively. If passing score is 63, at most how many people failed? _ ScoreJ? _ 6375 _ K S _ 8 _71.5 Now by Chebyshev' 5 Rule, at least (1 1 g) X 100 % = 55.55 % of the scores are within (X 41(5): (75 i 1 5 x 8): (63,.87) Hence at most (100 - 55.55) % = 44.45 % = 20 students failed. At most | At least | At most 1 1 1 15,. .100% | (1 752). 100% | 5,. .100% 65 87 3. Five people applied for two scholarships. Three of them are men and two are women. Two applicants are randomly chosen from them. (a) How many different choices are possible, write down the sample space. (Assume men and women are distinguish able). Let's say 3 men are (M1, M2, M3) and 2 women are denoted by (W1, W2). Number of elements in the sample space is = (a) = % : 10 Hence the Sample Space = S = {(M1,M2), (ll/11,1143), (M1,W1), (M1,W2), (M2,M3), (M21W1):(M2:W2)a(M37W1)1(M31W2)1(W11W2)} (b) What is the probability that two men are selected ? Due to random selection each pair is equally likely and hence probability of each pair chosen is %. The event , two men are selected = A = {(M1,M2), (M1,M3), (M2,M3)} P(A) = P{(M1,M2)} + P{(M1,M3)} + P{(M2,M3)} = % + 110 + 11_0 = 1% 4. In a small university, 60% of the students have taken statistics course. Two students are randomly selected from the student population, Let A1 = Student-1 has taken statistics and A2 = Student-2 has taken statistics Then P(A1) = 0.6 and 10042) = 0.5 What is the probability that (a) At least one of them has taken at least one statistics class. Let C = At least one of them has taken at least one statistics class = A1 U A2 P(C) = P(A1) + P(A2) P(A1 W12) = P(A1) + P(A2) P(A1) x P(A2) = 0.5 + 0.6 0.0 x 0.6 = 0.84 (b) None of them taken any statistics class. By above denition of C, C = None of them taken any statistics class. P(C' = 1 P(C) = 1 0.84 = 0.16