Of all the trees planted last year by a landscaping firm 10

Of all the trees planted last year by a landscaping firm, 10% died within a month. Suppose a new landscaping firm is hired to plannt 15 new trees. let X denote the number of tress planted (out of 15) that died.

a. what values of X suggest that the new landscaping company has a lower failure rate?

b. what values of X are consistent with the previous landscaping company\'s failure rate?

c. what values of X indicate that the new landscaping company has a higher failure rate than the previous contractor?

Solution

Let Y be the number of trees died out of 15 planted by the old firm.

Then Y~Bin(15,0.1)

Expected number of dead trees = E(Y) = 15 *0.1 = 1.5

(a)

X=0,1 suggest that the new landscaping company has a lower failure rate.

(b)

X=1,2 are consistent with the previous landscaping company\'s failure rate.

(c)

X=2,3,4,...,15 indicate that the new landscaping company has a higher failure rate than the previous contractor.