Check for Understanding AWS
Check for Understanding 1. A university claims that 80% of its basketball players get degrees. An investigation examines the fate of all 20 players who entered the program over a period of several years that ended six years ago. Of these players, 11 graduated and the remaining 9 are no longer in school. If the university’s claim is true, the number of players among the 20 who graduate should have the binomial distribution with n = 20 and p = 0.8. (a) Find the mean number of graduates out of 20 players. (b) Find the standard deviation 𝜎of the count X.
2. The owner of a small convenience store notices that only 5% of customers buy magazines. How many customers should the owner expect until a customer buys a magazine?
3. Larry the Luckless has written a new program in C++ that has computed his probability of being rejected by any particular young lady whom he invites to the prom to be .993. If his attempts are independent, what is the expected number of young ladies he must invite in order to achieve an acceptance? (A) 1 (B) 1.007 (C) 138 (D) 142.857 (E) 155
Answers 1a. The mean is 16 players (np = 20*0.8 = 16) 1b. The standard deviation is approximately 1.7888 (standard deviation is the square root of n times p times (1 – p). In this case, the square root of 20 * 0.8 * 0.2.) 2. The expected value is 20. For a geometric setting, the expected value is 1 / p. In this case 1 / 0.05 is 20 3. The correct answer is D. For a geometric setting, the expected value is 1/p. In this case, p is the probability of success, which is not .993, but 1 - .993, or .007. So, 1/.007 = 142.857.
2. The owner of a small convenience store notices that only 5% of customers buy magazines. How many customers should the owner expect until a customer buys a magazine?
3. Larry the Luckless has written a new program in C++ that has computed his probability of being rejected by any particular young lady whom he invites to the prom to be .993. If his attempts are independent, what is the expected number of young ladies he must invite in order to achieve an acceptance? (A) 1 (B) 1.007 (C) 138 (D) 142.857 (E) 155
Answers 1a. The mean is 16 players (np = 20*0.8 = 16) 1b. The standard deviation is approximately 1.7888 (standard deviation is the square root of n times p times (1 – p). In this case, the square root of 20 * 0.8 * 0.2.) 2. The expected value is 20. For a geometric setting, the expected value is 1 / p. In this case 1 / 0.05 is 20 3. The correct answer is D. For a geometric setting, the expected value is 1/p. In this case, p is the probability of success, which is not .993, but 1 - .993, or .007. So, 1/.007 = 142.857.
