Can you help me with problem 5.2

5.1 The Probability Distribution for a Discrete Variable 179 Table 5.3 shows all intermediate steps for calculating the variance and the standard deviation of the number of interruptions per day using Equations (5.2) and (5.3). o' = _ [x, - E(X)P P(X = x) = 0.686 + 0.040 + 0.072 + 0.256 + 0.338 + 0.648 = 2.04 and ( = Vo' = V2.04 = 1.4283 TABLE 5.3 Calculating the variance Interruptions and standard deviation per Day (x;) P(X = x;) x;P(X = x;) [x; - E(X)] [x, - E(X)IP(X = x;) of the number of 0.35 0.00 (0 - 1.4) = 1.96 (1.96)(0.35) = 0.686 interruptions per day 0.25 0.25 (1 - 1.4) = 0.16 (0.16)(0.25) = 0.040 0.20 0.40 (2 - 1.4) = 0.36 (0.36)(0.20) = 0.072 0.10 0.30 (3 - 1.4) = 2.56 (2.56)(0.10) = 0.256 0.05 0.20 (4 - 1.4) = 6.76 (6.76)(0.05) = 0.338 5 0.05 0.25 (5 - 1.4) = 12.96 (12.96)(0.05) = 0.648 1.00 u = E(X) = 1.40 0? = 2.04 0 = Vo' = 1.4283 Thus, the mean number of interruptions per day is 1.4, the variance is 2.04, and the standard deviation is approximately 1.43 interruptions per day. PROBLEMS FOR SECTION 5.1 LEARNING THE BASICS Number of Accidents 5.1 Given the following probability distributions: Daily (X) P(X = x1) D. 10 Distribution A Distribution B 0.20 P(X = x) P(X = x;) 0.45 0.50 0.05 0.15 0.20 0.10 0.05 0.15 0.15 0.05 AWN - 0.10 0.20 a. Calculate the mean number of accidents per day. 0.05 0.50 b. Calculate the standard deviation. c. What is the probability that there will be at least two accidents a. Calculate the expected value for each distribution. on a given day? b. Calculate the standard deviation for each distribution. c. What is the probability that x will be at least 3 in Distribution A 5.3 Recently, a regional automobile dealership sent out fliers to and Distribution B? prospective customers indicating that they had already won one of d. Compare the results of distributions A and B. three different prizes: an automobile valued at $25,000, a $100 gas card, or a $5 Walmart shopping card. To claim his or her prize, a APPLYING THE CONCEPTS prospective customer needed to present the flier at the dealership's showroom. The fine print on the back of the flier listed the prob- SELF 5.2 The following table contains the probability distri- abilities of winning. The chance of winning the car was 1 out of TEST bution for the number of traffic accidents per day in a 31,478, the chance of winning the gas card was 1 out of 31,478, and small town: the chance of winning the shopping card was 31,476 out of 31,478