Suppose the Profit Potential Y of SpongeBob Squarepants Unde

Suppose the Profit Potential (Y) of SpongeBob Squarepants Underwear 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 and drills 6 teeth at random. What is the probability that fewer than 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 the second time on the fifteenth shot.

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

   .   4 In a certain desert region the number of persons who become seriously ill from eating a certain poisonous plant is a random variable having a Poisson distribution with.

a)What percent of the time would you expect the number of illnesses to be less than one standard deviation below the mean?

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

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

Solution

Q6.

Binomial Distribution

PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial

P( X = 3 ) = ( 30 3 ) * ( 0.04^3) * ( 1 - 0.04 )^27
= 0.0863