G Competetiv X Theory of C X Price elastic X G demand fur X supply and X i Demand Cu X GERS A4-22.pdf X Homework X + V X C PDF Viewer | chrome-extension://oemmndcbudboiebfnladdacodfmadadm/https://brightspace.nyu.edu/d21/common/viewFile.d2lfile... A 06HOBUTb t 1 N13 3 + ABTOMaTN4ecKN Problem 1 (10) A drug manufacturer claims that a new drug for lowering blood pressure is effective in 80% of patients. Consider a random sample of 20 patients. Use the information provided by a manufacturer to compute a) the probability that the drug will be effective in 15 to 18 patients. (3) b) the probability that the drug will be effective in at least 8 patients? (3) c) the expected number of patients and the standard deviation of the number of patients for which the drug will not be effective. (2) d) When the drug was tested it lowered blood pressure in 7 out of 20 patients. In view of this, what do you think about manufacturer's claim concerning the rate of the effectiveness of the drug? (Justify your answer) (2) LO O EN 22:02 15.C Clear ~ 0 () LJ 14.10.2022G Competetiv X Theory of C X Price elastic X G demand fur X supply and X i Demand Cu X GERS A4-22.pdf X Homework X + V X C PDF Viewer | chrome-extension://oemmndcbudboiebfnladdacdfmadadm/https://brightspace.nyu.edu/d21/common/viewFile.d2lfile... [ A 06HOBNTb 2 N13 3 + ABTOMaThyecKN Problem 2 (8) A customer at Shorebank is called a "frequent ATM user" if he / she uses an ATM (Automated Teller Machine) for majority of her/his transactions. Accord- ing to bank records, 30% of all Shorebank customers are frequent ATM users. To improve services at the bank a team of researchers has decided to form a customer focus group by choosing six customers at random. a) One member of the team hopes that at least two members of the fo- cus group will be frequent ATM users. What is the probability of this event happening? (3) b) Another member of the team hopes that at least two members of the focus group will be infrequent ATM users. What is the probability of this event happening? (2) c) What is the probability that the focus group will satisfy both members wishes? (will have at least two frequent and two infrequent ATM users) (3) Problem 3 Tax returns audited by the IRS (10) MBS, Ex 4.56, page 217. a) (2) b) (2 ) c) (2 ) d) (3) e) (1) Problem 4 (3) MBS, Ex 4.156a) on page 255. Evaluating risk in a new product line. Hint. The uniform distribution in question extends over an interval from 0 EN LO O B 90 m P w ] 22:03 15.C Clear ~0 0 () LJ 14.10.2022G Competetiv X Theory of C X Price elastic X G demand fur X supply and X i Demand Cu X GERS A4-22.pdf X Homework X + V X C PDF Viewer | chrome-extension://oemmndcbudboiebfnladdacodfmadadm/https://brightspace.nyu.edu/d21/common/viewFile.d2lfile... [ A 06HOBUTb 2 N13 3 + ABTOMATNeckN e) (1) Problem 4 (3) MBS, Ex 4.156a) on page 255. Evaluating risk in a new product line. Hint: The uniform distribution in question extends over an interval from 0 to b, and one has to determin b. Problem 5 (4) Helen has an early class tomorrow, She knows that she needs to get to bed by 10:00 p.m. in order to be rested the next day. However, before she goes to bed she must complete a homework assignment which is due tomorrow morning. According to her experience the time it takes her to complete an assignment is normally distributed with mean 3.5 hours and standard deviation 1.2 hours. It is now 6 p.m. What is the probability that she will be able to get to bed at 10 p.m.? Problem 6 (10) The management of a supermarket knows from the past experience that ex- penditures per customer are normally distributed with mean of $95 and standard deviation of $21 a) What is the probability that a randomly selected customer will spend between $85 and $105? (2) 2 EN LO O EM 22:03 15.C Clear ~ 0 () LJ 14.10.2022G Competetiv X Theory of C X Price elastic X G demand fur X supply and X i Demand Cu X GERS A4-22.pdf X Homework X + V X C PDF Viewer | chrome-extension://oemmndcbudboiebfnladdacdfmadadm/https://brightspace.nyu.edu/d21/common/viewFile.d2lfile... A 06HOBUTb t 3 13 3 + ABTOMaTN4ecKN b) The management plans to give a bonus to the customers whose expendi- tures are in the top 20% of the distribution of expenditures per customer. What is the least expenditure that qualifies a customer for a bonus? (3) c) Consider a random sample of 4 customers. What is the probability at least one customer's expenditures will be above the 80th percentile of the distribution of expenditures per customer? (3) d) Consider a random sample of 100 customers. What is the expected num- ber customers and standard deviation of the number of customers whose expen- ditures will be above the 80th percentile of the distribution of expenditures per customer? (2) EN LO O 22:04 15.C Clear ~ 0 E () 14.10.2022