Question

Question 6 Incorrect 0.0o points out of 400 Flagquestion Assume that about 40% of all US adults try to pad their insurance claims. Suppose that you are the director of an insurance adjustment office. Your office has just received 108 insurance claims to be processed in the next few days. What is the probability that fewer than 40 of the claims have been padded? Select one a. 0.766 b. 0265 C. 0.735 d. 0.298 e. 0.234 Type here to search 8 6 O.

Answer 1

answer:

given data,

$\Rightarrow$p is 40%

$\Rightarrow$ probability is 40/100 = 0.40

$\Rightarrow$n is 140

$\Rightarrow$the Normal approximation to the Binomial distribution to be used.

$\Rightarrow$the Expectation is  np $\Rightarrow$43.2

$\Rightarrow$the Variance is  np(1 - p) $\Rightarrow$ 29.6

$\Rightarrow$Standard deviation is 5.4222

$\Rightarrow$the Z value for 38, z =(40-43.2)/5.4222

$\Rightarrow$ -3.2/5.4222

$\Rightarrow$-0.590

$\Rightarrow$ -0.59 P( x < 40)

$\Rightarrow$ P( z < -0.59)

$\Rightarrow$0.2779 Alternate answer: If we are use to the Binomial distribution,

$\Rightarrow$P( x <38)

$\Rightarrow$0.234

$\Rightarrow$therefore 0.234

$\Rightarrow$so fainally the answer is option e is correct answer

0.234