1) You run a simple statistical experiment that consists of tossing a fair, balanced coin twice.Answer questions A to I based on this experiment.

A) Define a random variable X which is equal to the number of heads occurring on the two-coin tosses.Create probability distribution table showing the possible values of X and the probability of getting each of those values.Explain why your probability distribution is valid (remember there are two conditions).

B) Create graph showing the probability distribution you created in question B.

C) Is this random variable Discrete or Continuous?

D) What is the probability that x = 0?

E) What is the probability that x is greater than or equal to 1?

F) What is the probability that x is greater than 2?

G) Use the formula to compute E(x).

H) Compute ², the variance of x.

I) Compute , the standard deviation of x.

2) Assume that 70% of City College students own smartphones.You pick 20 CCSF students at random and find out if each of them owns a smartphone.Use this experiment to answer questions i to vii.

i) Compute the probability that exactly 12 students in your sample own smartphones.Use the formula and show your work.

ii) Compute the probability that the number of students in your sample who own smartphones is less than or equal to 16.Use the table to find the answer.

iii) Compute the probability that more than 16 students in your sample own smartphones.

iv) Compute the probability that exactly 16 students in your sample own smartphones.

v) Compute E(x).

vi) Compute Var (x) = ².

vii) Compute , the standard deviation.

3) Assume that you run a call center that receives an average of 3 calls per minute with a Poisson distribution.Use this information to answer questions a to d.

a.What is the probability that the call center receives exactly 2 calls in the next minute?Use the formula and show your work.

b.What is the probability that the call center receives exactly 4 calls in the next minute?

c.What is the probability that the call center receives exactly one call in the next 20 seconds?

d.What is the probability that the call center receives 2 or more calls in the next 20 seconds?

4) A particular industry has 15 companies.At the beginning of the year you picked ten of these companies at random and bought stock in these ten companies.During the year a total of 11 of the companies in the industry made a profit and 4 made a loss.What is the probability that exactly 7 of the companies you bought stock in made a profit during the year?