It is believed to be true that 15% of the U.S. population is left-handed. You randomly select 7 people. Let r represent the number of left-handers.

a.(8 pts) Construct the binomial probability distribution.(Show 3 decimal places or as many as it takes to get to one non-zero digit.)

Show calculator function and inputs used!!

(b-d) (12 pts) State answers using mathematical notation in terms of r. (For example, notation for "b" would be P(r=5) =_________ ) Find the probability that:

b.exactly 5 people are left-handed. ____________________________________

c.less than 3 people are left-handed. ____________________________________

d.at least one person is left-handed. ____________________________________

e.(6 pts) Find the mean and standard deviation of the binomial distribution. (Show/explain your work and use correct symbols for your answers. Round to the nearest hundredth, if applicable.)

Mean = (symbol) ________ __________Standard Deviation = (symbol) ________ __________

f.(4 pts) Keep in mind that your book defines unusual as "more than 2.5 standard deviations from the mean". In a random sample of 7 people, would it be unusual to select 4 who are left-handed? __________ Show your work.