PROBLEM-1 Prof. Hardtack gave four Friday quizzes last semester in his 10 student senior tax accounting class. Find the mean, standard deviation and coefficient of variation for each quiz. a) How do these data sets differ in terms of Central Tendency and Dispersion? b) Briefly describe and compare student performance on each quiz. Quiz 60 60 60 60 71 73 74 75 88 99 1 Quiz 65 65 65 65 70 74 79 79 79 79 2 Quiz 66 67 70 71 72 72 74 74 95 99 3 Quiz 10 49 70 80 85 88 90 93 97 98 4
A multinational bank issuing Master Card is monitoring the use of credit card account holders in the context of their spending habits. A market survey shows that the average monthly spending of it’s regular card users is normally distributed with mean Rs.2800 and standard deviation Rs.900. The customers are classified into four categories according to pattern of spending: a. b. c. d. Category 1 spends less than Rs.2000. Category 2 spends Rs.2000 or more but less than Rs.3000. Category 3 spends Rs.3000 or more but less than Rs.4000. Category 4 spends Rs.4000 or more. What proportion of customers would you expect to fall into each category?
The foreman of a bottling plant has observed that the amount of soda in each 32 ounce bottle is actually a normally distributed random variable with a mean of 32.2 ounce & S.D of 0.3 ounce. A) If a customer buys 1 bottle, what is the probability that the bottle will contain more than 32 ounce? B) If a customer buys a carton of 4 bottles, what is the probability that the mean amount of 4 bottles will be greater than 32 ounce?
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PROBLEM 4(A) & 4(B)
(A) A manufacturer of automobile batteries claims that the distribution of the lengths of life of its battery has a mean of 54 months & a S.D of 6 months. Suppose a consumer group decides to check the claim by purchasing a sample of 50 0f these batteries & subjecting them to tests that determine their lives. Assuming that the manufacturer’s claim is true, what is the probability that the consumer group’s sample has an average life of 52 or fewer months? (B) For assessing the number of monthly transactions in credit cards issued by a bank, transactions in 25 cards were analyzed. The analysis revealed an average of 7.4 transactions and sample standard deviation of 2.25 transactions. Find confidence limits for the monthly number of transactions by all the credit card holders of the bank.
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• A certain type of bacteria occurs in all raw milk. • Let X denote the bacteria count per ml of milk. • The public health department has found that if the milk is not contaminated, then X has a distribution that is more or less bellshaped and symmetric with mean µ=2550 & the S.D ơ= 300. • In a large commercial dairy, the health inspector takes 42 random samples of milk produced each day. • At the end of the day the bacteria count in each of the 42 samples is averaged to obtain the sample average bacteria count X. • A) Assuming that the milk is not contaminated, what is the distribution of X? • B) Assuming that the milk is not contaminated, what is the probability that the sample average bacteria count X for one day is between 2400 & 2700 bacteria /ml? • C) At the end of each day, the inspector must decide whether to accept or reject the accumulated milk that has been held in cold storage awaiting shipment. Suppose the 42 samples taken by the inspector have a men bacteria count X that is not between 2400 & 2700. If you were the inspector what would be your comment on these situation?
The director of a market research agency wishes to study the reach of a particular advertising campaign. He is concerned with the percentage of the target market that has seen at least a portion of the campaign. The director does not think that the figure will exceed 25%. What should be the sample size for this study if the director wishes the estimate to be within three percentage points of the true value and 95%...
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