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##### Week 4 homework problem2

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Question;Given a standardized normal;distribution (with a mean;of 0 and a standard deviation of 1;as in Table E.2), what is;the probability that;a. Z is less than 1.57?;b. Z is greater than 1.84?;c. Z is between 1.57 and 1.84?;d. Z is less than 1.57 or greater;than 1.84?;Given a normal distribution with ?= 100 and?= 10;what is the probability that;a.;x > 75;b.;x < 70;c.;x 110;d. Between what two X values (symmetrically distributed;around the mean) are 80% of the values?;In 2008, the per capita consumption of coffee in the United;States was reported to be 4.2 kg, or 9.24 pounds (data extracted from;en.wikipedia.org/wiki/List_of_countries_ by_coffee_consumption_per_capita).;Assume that the per capita consumption of coffee in the United States is;approximately distributed as a normal random variable, with a mean of 9.24;pounds and a standard deviation of 3 pounds.;a. What is;the probability that someone in the United States consumed more than 10 pounds;of coffee in 2008?;b. What is;the probability that someone in the United States consumed between 3 and 5;pounds of coffee in 2008?;c. What is;the probability that someone in the United States consumed less than 5 pounds;of coffee in 2008?;d. 99% of;the people in the United States consumed less than how many pounds of coffee?;Consumers spend an average of $21 per week in cash without;being aware of where it goes (data extracted from ?Snapshots: A Hole in Our;Pockets,? USA Today, January 18, 2010, p. 1A). Assume that the amount of cash;spent without being aware of where it goes is normally distributed and that the;standard deviation is $5.;a. What is;the probability that a randomly selected person will spend more than $25?;b. What is;the probability that a randomly selected person will spend between $10 and $20?;c. Between;what two values will the middle 95% of the amounts of cash spent fall?;A statistical analysis of 1,000 long-distance telephone;calls made from the headquarters of the Bricks and Clicks Computer Corporation;indicates that the length of these calls is normally distributed, with ?= 240;seconds and?= 40seconds.;a. What is the probability that a call lasted less than 180;seconds?;b. What is the probability that a call lasted between 180;and 300 seconds?;(c) How many calls lasted less than 180 seconds;or more than 300 seconds?;d. What is the probability that a call lasted between 110;and 180 seconds?;e. 1% of all calls will last less than how many seconds?;The following table;contains the probabilitydistribution for the number of traffic accidents daily in a small city;Number of Accidents Daily (X);P1X = xi2;0;0.1;1;0.2;2;0.45;3;0.15;4;0.05;5;0.05;a. Compute the mean;number of accidents per day.;b. Compute the;standard deviation.;Q If n=5 and p = 0.40,what is the probability that;Q-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 is distributed as a binomial random variable.;a. What are the mean and standard deviation of the number;of customers exceeding their credit limits?;b. What is the probability that zero customers will exceed;their limits?;c. What is the probability that one customer will exceed his;or her limit?;d. What is the probability that two or more customers will;exceed their limits?;Q-5.21;Assume that the number of network errors experienced in a;day on a local area network (LAN) is distributed as a Poisson random variable.;The mean number of network errors;experienced in a day is 2.4. What is the that in any given day;a. zero network errors will occur?;b. exactly one network error will occur?;c. two or more network errors will occur?;d. fewer than three network errors will occur?;Q;The quality control manager of Marilyn?s Cookies is;inspecting a batch of chocolate-chip cookies that has just been baked. If the;production process is in control, the mean number of chip parts per cookie is;6.0. What is the probability that in any particular cookie being inspected;a.;fewer than five chip parts will be found?;b.;exactly five chip parts will be found?;c. five;or more chip parts will be found?;d.;either four or five chip parts will be found?

Paper#62151 | Written in 18-Jul-2015

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