Question

In Hawaii, January is a favorite month for surfing since 60% of the days have a surf of at least 6 feet.† You work day shifts in a Honolulu hospital emergency room. At the beginning of each month you select your days off, and you pick 5 days at random in January to go surfing. Let r be the number of days the surf is at least 6 feet.

(a) Make a histogram of the probability distribution of r.

(b) What is the probability of getting 4 or more days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(c) What is the probability of getting fewer than 2 days when the surf is at least 6 feet? (Round your answer to three decimal places.)


(d) What is the expected number of days when the surf will be at least 6 feet? (Round your answer to two decimal places.)
days

(e) What is the standard deviation of the r-probability distribution? (Round your answer to three decimal places.)
days

(f) Can you be fairly confident that the surf will be at least 6 feet high on one of your days off? Explain. (Round your answer to three decimal places.)

---Select--- Yes No , because the probability of at least 1 day with surf of at least 6 feet is  and the expected number of days when the surf will be at least 6 feet is  ---Select--- greater than equal to less than one.

Answer 1

a)

b)

P(X>=4)=1-P(X<=3)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.337

c)

P(X<2)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.087

d)

mean E(x)=μ=np=3

e)

standard deviation σ=√(np(1-p))=1.095

f)

Yes because the probability of at least 1 day with surf of at least 6 feet is 0.990 and the expected number of days when the surf will be at least 6 feet is greater than one