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ACTIVITY 1: In a convenient store, the number of teller (X) busy with customers at 12:00 noon varies from day to day. Past records indicate that the probability distribution of X is as follows: Soboo rbisori Number of Teller X Probability P(x) 0 0.029 1 0.049 2 0.078 3 0.155 oiv 0.212 0.262 0.215 Questions: 1. What is the probability that exactly four tellers are busy at 12:00 noon? noitsiweb bisbase wh bris sonchev ords sis said // no 2. What is the probability that at least two tellers are busy at 12:00? 3. What is the probability that fewer than five tellers are busy at 12:00? :& divinA lang sili grib nolimogo? 1010M A is vab isq bloa zino lo isdmun shi sis gniwolfof srT .evsb gothow 002 4. What is the probability that at least, but fewer than five tellers are busy at 12:00 noon? 0 79d mul. (7.) 0 5. What is the mean of the probability distribution? S dd A 6. What is the standard deviation of the probability distributions? 2 ACTIVITY 2: 2 Solve the following problems.c health code in a ' 1. The probabilities that a market inspector will discover violatiOns of the Pub11 pubhc market are given in the following table "~ '7.- Number of violations X _ _a_ 3 __ ____ . d: a_ 3- What is the Pmbability that a market inspector will discover, at least, two violations of the public ' healthcodc? ' ' "' _ " " b. What is the probability th_ ta 'yrnarlg'et inspector} will discover; atI lino-st; three violations of the public r health code? , . _, c. What is the probability that a market inspector Will discover at least two, but fewer than four ' ' violations of the public health code? - - - - -- 7 , r- 1' d What is the mean of the probability distribution? , . _ : ,; A e. What are the variance and the standard deviation of the probability distribution?\" : .l i _ . . V . - _-| v . . _ '. 1 V. ' I' I . . , -"5 'i"/..I": iif :i' '. Activity3: ..-+,~n.: 2. The following are the number of cars sold per day at ABC Motor Corporation during the past 500 working days. a. What is the probability that exactly four cars will be sold at a given day? b. What is the probability that, at most, four cars will be sold at a given day? c. What is the probability that at least six, but at most ten cars will be sold at a given day? d. What is the probability that fewer than eight cars, but greater than three cars will be sold at a given day? e. What is the expected number of cars that will be sold at a given day? f. What is the standard deviation of the number of cars that will be sold at a given day? ACTIVITY 4: Find the mean, the variance and the standard deviation of the following probability distribution. X P(X) 2 0.001 4 0.071 5 0.094 16 0.138 7 0.229 8 0.246 9 0.118 10 0.103 Solutions:Analyze and Explore The mean or expected value of probability tells the value of a random variable that we expect to get if the experiment is done repeatedly. In other words, if the experiment or process is repeated long enough, there is a likelihood or chance that the average of the outcomes will begin to approach the expected value or the mean value The standard deviation of probability distribution indicates how far, on the average, is an observed value of random variable X from its mean. The smaller the standard deviation, the more likely that an observed value of the random variable will be close to its mean. Use this concepts to solve problems involving the mean and the variance of the probability distribution as in the examples that follow. EXAMPLE 1: The following data show the probability distribution of the number of computers sold daily in a computer shop during the past several months. Number of Computer (X) Probability P(X) 0 0.10 0.20 12 0.45 3 0.15 14 0.05 0.05 Questions: 1. What is the probability that on a given day------ a. Fewer than three computers will be sold? b. At most, two computers will be sold? c. At least, four computers will be sold? d. Exactly three computers will be sold? e. Find the mean f. Find the standard deviation of the probability distribution Solutions: To find the probabilities----- a. To find the probability that fewer than three computer will be sold, use X= 0,1, and 2. P(x