Question

Assume that about 30% of all U.S. adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 140 insurance claims to be processed in the next few days. What is the probability that from 45 to 47 of the claims have been padded?

a. 0.222
b. 0.167
c. 0.119
d. 0.104
e. 0.056

Answer 1

For x=45

sample proportion=45/140=0.321

z=(0.321-0.30)/sqrt(0.3*(1-0.3)/140)

z=0.54

For x=47

sample proportion=47/140=0.336

z=(0.336-0.30)/sqrt(0.3*(1-0.3)/140)

z=0.93

Now,

P(0.54<z<0.93)=P(z<0.93)-P(z<0.54)

=0.8238-0.7054

=0.118

So,correct option is 0.119