Math 3C Sample Final.pdf

# B if two independent tests are performed and both are

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(b) If two independent tests are performed and both are positive, what is the probability that the individual has the disease? 4. (8 points) In a gambling game, a loaded coin is tossed with a probability 1/2 + p to show the head. The rule of the game is that if the head shows up, the player gets \$5, and otherwise he pays \$4. (a) What the expected amount to return if the game is played once? (Express the result in terms of p) (b) The game is planned to play 100 times. How does the player need to load the coin (i.e. to determine p) in order to make his expected return be \$200? 5. (10 points) A random variable has the following probability density function: for 0 ::; x ::; b otherwise (a) Determine b. (b) Find the mean and the variance. 6. (10 points) Suppose the heights of children in a school follow a normal distribution with a mean of 150 cm and a standard deviation of 20 cm. (a) Find the probability that a child randomly chosen from this population has a height between 130 cm and 160 cm. (Consult the Table at the end and round your answer to the nearest hundredth.) (b) Select randomly 10 children, find the probability that at least one child's height is between 130 cm and 160 cm. (Simplify as mush as you can given you do not have a calculator.) 7. (10 points) How often have you toss a coin to determine P(heads) within 0.1 of its true value with probability at least 0.9.

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