Question

The customer service department for a wholesale electronics outlet claims that 80 percent of all customer complaints are resolved to the satisfaction of the customer. In order to test this claim, a random sample of 15 customers who have filed complaints is selected.

(b)	Find each of the following if we assume that the claim is true: (Do not round intermediate calculations. Round final answers to 4 decimal places.)

1.	P(x ≤ 13)
2.	P(x > 10)
3.	P(x ≥ 14)
4.	P(9 ≤ x ≤ 12)
5.	P(x ≤ 9)

(c)	Suppose that of the 15 customers selected, 9 have had their complaints resolved satisfactorily. Using part b, do you believe the claim of 80 percent satisfaction? Explain.

  (Click to select)NoYes ; if the claim is true, then P(x ≤ 9) is very (Click to select)smalllarge .

Answer 1

a)

here this is binomial with parameter n=15 and p=0.8

b)

1)

P(X<=13)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.8329

2)

P(X>=11)=1-P(X<=10)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.8358

3)

P(X>=14)=1-P(X<=13)=

1-∑x=0x-1   (nCx)px(q)(n-x) =

0.1671

4)

P(9<=X<=12)=

∑x=ab     (nCx)px(1−p)(n-x)    =

0.5839

5)

P(X<=9)=

∑x=0a     (nCx)px(1−p)(n-x)    =

0.0611

c)

no if the claim is true, then P(x ≤ 9) is very small