Suppose the Profit Potential (Y) of SpongeBob SquarepantsUnderwear has the following distribution:

Y -100 50 200

P(y) .30 .40 .30

Find a) expected profit

b) variance of Profit:

. 2. X-rays show that 6 of Patrick’s 32 teeth have cavities. Unfortunately, Patrick’s dentist, Al Yankum, is somewhat myopic anddrills 6 teeth at random. What is the probability that fewerthan 2 cavities are properly drilled?

3An expert sharpshooter misses a target 5% of the time.

a) Find the probability that she will miss the target for thesecond time on the fifteenth shot.

b) How many shots would you expect her to take to get 10 shots ontarget?

. 4 Ina certain desert region the number of persons who become seriouslyill from eating a certain poisonous plant is a random variablehaving a Poisson distribution with.

a)What percent of the time would youexpect the number of illnesses to be less than one standarddeviation below the mean?

5If X has the cumulative distribution as follows find theprobability distribution function.

6. A study indicates that 4% of American teenagers havetattoos. You randomly sample 30 teenagers. What is the likelihood that exactly 3 will have atattoo?