a. Let x=the number of sampled customers whose complaints were resolved to the customer’s satisfaction. Assuming the claim is true, write the binomial formula for this situation.
b. b Use the binomial tables (see Table A.1, page 783) to find each of the following if we assume that the claim is true:
(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 90 percent satisfaction? Explain.
METHODS AND APPLICATIONS
5.30 Suppose that x has a Poisson distribution with u= 2.
a Write the Poisson formula and describe the possible values of x.
b Starting with the smallest possible value of x, calculate p(x) for each value of x until p(x) becomes smaller than .001.
c Graph the Poisson distribution using your results of b.
d Find P(x=2).
g Find P(x>1) and P (x>2).
i Find P(2<x<5).
e Find P(x<4).
h Find P(1<x<4).
j Find P(2<x<6).
f Find P(x<4).
METHODS AND APPLICATIONS
6.6 Suppose that the random variable x has a uniform distribution with c = 2 and d = 8.
a Write the formula for the probability curve of x, and write an interval that gives the possible values of x.
b Graph the probability curve of x.
c Find P(3<x<5).
d Find P(1.5 < x < 6.5).
e Calculate the mean μ, variance σ2, and standard deviation σX.
f Calculate the interval [μ + 2 σX]. What is the probability that x will be in this interval?
6.26 Suppose that the random variable x is normally distributed with mean μ= 1,000 and standard deviation σ2 =100. Sketch and find each of the following probabilities:
a P(1,000<x<1,200)
b P(x>1,257)
c P(x < 1,035)
d P(857<x<1,183)
e P(x<700)
f P(812<x<913)
g P(x > 891)
h P(1,050 <x<1,250)
6.54 Suppose that the random variable x has an exponential distribution with λ = 2.
a Write the formula for the exponential probability curve of x. What are the possible values of x?
b Sketch the probability curve.
c Find P(x < 1).
d FindP(.25 <x <1).
e Find P(x > 2).
f Calculate the mean, μx , the variance, σx2, and the standard deviation, σx, of the exponential distribution of x.
g Find the probability that x will be in the interval [μx + 2 σx].