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Statistics Questions




Question;5.9) Determine the following;A) for n = 4 and? = 0.12, what is P(X = 0)?;B) for n = 10 and? = 0.40, what is P(X = 9)?;C) for n = 10 and? = 0.50, what is P(X = 8)?;D) for n = 6 and? = 0.83, what is P(X = 5)?;5.15) when a customer places an order with Rudy?s On-;Line Office Supplies, a computerized accounting information system (AIS) automatically checks to see if the customer has exceeded his or her credit limit. Past records indicate that the probability of customers exceeding their credit limit is 0.05. Suppose that, on a given day, 20 customers;place orders. Assume that the number of customers that the AIS detects as having exceeded their credit limit ism distributed as a binomial random variable.;a. What are the mean and standard deviation of the numberof customers exceeding their credit limits?;b. What is the probability that zero customers will exceed their;limits?;c. What is the probability that 1 customer will exceed his or her limit?;d. What is the probability that 2 or more customers will exceed their limits?;5.17)In example 5.4 on page 187,you and two friends decided to go to;Wendy?s.Now,suppose that instead you go to McDonald?s,which last month filled;approximately 90.1% of the orders correctly. What is the probability that;a).all three orders will be filled correctly?;b). none of the three will be filled correctly?;c). at least two of the three will be filled correctly?;d. What are the mean and standard deviation of the binomial distribution used;in (a) through (c)? Interpret these values.;e. Compare the result of (a)-(d) with those of Popeye?s in Problem 5.26 and;Wendy?s in Example 5.4 on page 203;EXAMPLE 5.4;Computing;Binomial;Probabilities;Accuracy in taking orders at a drive-through window is important for fast-food;chains.;Periodically, QSR Magazine (data extracted from;;drive-thru_time_study/2009/2009_charts/whats_your_preferred_way_to_order_fast;food.html) publishes the results of its surveys. Accuracy is measured as the;percentage of orders;that are filled correctly. Recently, the percentage of orders filled correctly;at Wendy?s;was approximately 89%. Suppose that you go to the drive-through window at;Wendy?s and;place an order. Two friends of yours independently place orders at the;drive-through window;at the same Wendy?s. What are the probabilities that all three, that none of;the three, and that;at least two of the three orders will be filled correctly? What are the mean;and standard deviation;of the binomial distribution for the number of orders filled correctly?;SOLUTION Because there are three orders and the probability of a correct order;is;and Using Equations (5.6) and (5.7);VARIANCE OF THE SUM OF TWO RANDOM VARIABLES;(5.6);STANDARD DEVIATION OF THE SUM OF TWO RANDOM VARIABLES;sX+Y = 2s (5.7);Using Equation (5.11) on page 192;= 110.89210.89210.892112 = 0.7050;=;3!;3!13 - 32!;10.892310.1120;P1X = 3|n = 3, p = 0.892 =;3!;3!13 - 32!;10.892311 - 0.8923-3;= 20.2937 = 0.5419;= 2310.89210.112;s = 2s2 = 2Var1X2 = 2np11 - p2;m = E1X2 = np = 310.892 = 2.67;0.89, n = 3 p = 0.89


Paper#60430 | Written in 18-Jul-2015

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