4) In a game of roulette, a wheel spins and a ball randomly falls into one of 38

Question

4) In a game of roulette, a wheel spins and a ball randomly falls into one of 38 slots, each of them with a unique number. The ball is equally likely to fall into any of the slots. If you bet on lucky number 13, you will receive $180. But before you may set the ball into motion, you must pay $5 What isw the expected value of the game? Is it in your favor or the favor of the people running the game? 5) In a student population, 23% have 20-20 vision. In a randomly selected group of 36 students, what is the mean and standard devation of the number of 20-20 vision in the group? 6) The lengths of human pregnancies are normally distributed with a mean of 268 days and a standard deviation of 15 days. What is the probability that a pregnancy lasts at least 300 days? 7) The board of examiners that administers the real estate broker's examination in a certain state found that the mean score on the test was 557 and the standard deviation was 12. a) If the board wants to set the passing score so that only the best 10% of all applicants pass what minimum passing score should they set? o b) If the board wants to set the passing score so that only the worst 20% of all applicants do not pass, what is the minimum passing score should now? ire 8) The annual precipitation amounts in a certain mountain range are normally distributed of 107 inches, and a standard deviation of 12 inches. What is the probability with a mean that,the mean annual precipitation during 36 randomly picked years will be less than 109.8 inches? 9) A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, Are you planning or not planning to pursue a graduate degree? Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree

Explanation / Answer

Question 4:

As each of the 38 numbers are equally likely, therefore, we have here:

P( win ) = 1/ 38

The expected winnings here are therefore computed as:

= -5 + (180)P(win)

= -5 + (180)*(1/38) = -$0.26

Therefore -$0.26 is the expected value of the game here.

As the expected value here is negative this means that it is in favor of the people running the game.

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