Question

7. A carnival game costs $6 to play. The probability of winning is 0.25 and the prize is $30. Let x be the gain or loss of the player each time the game is played. Find the expected value or mean value of x.

8. Find the standard deviation of the following discrete probability distribution.

A=0.1

x P(x)

0 A

1 0.4

2 1-A

9. A bag contains 1 green marble and 3 red marbles. 3 times a marble is removed from the bag, its color noted, and then returned. Success is getting a green marble. Find the probability of getting three green marbles.

10. A population has a mean of 60 and a standard deviation of 61. Samples of size 100 are randomly selected. Calculate the standard deviation of the sample distribution X.

11. Tires are found to have a mean life of 800 hours. The standard deviation is 160. A sample of 100 is chosen. Find the probability that 40, 800 < X < 812.

12. A sample of size 100 is chosen from a population. The sample mean is 50 and the standard deviation is 10. Find the upper limit of the 95% confidence interval for the population mean.

Answer 1

7.

E(X) = 0.25*30 - 0.75*6

= 3

8.

1 2 3 4 х 0 1 2 P(X) 0.1 0.4 0.5

In order to find the standard deviation of the given distribution, we will use the following formula: orv 22. p(x) – 2 In this example: 5 (use "Find the Mean" option in this calculator for the step-by-step explanation on how to find mean) Now we will find the sum: 2 1 10 +12 +22 1 2 5 22. p(q) = 02. 22. p(x) = 12 5 Putting all together we have: 11 = 22 • p(x) – u2 = V-C) 0.6633

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