Assume that about 45% 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 110 insurance claims to be processed in the next few days. What is the probability that fewer than 45 of the claims have been padded?
0.778
0.831
0.194
0.806
0.169
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To determine the probability that fewer than 45 of the claims have been padded, we can use the binomial probability formula.
The binomial probability formula is:
P(X < k) = ∑(i=0 to k-1) (nCi) * p^i * (1-p)^(n-i)
Where:
P(X < k) is the probability of X being less than k
n is the number of trials or claims (110 in this case)
k is the number of claims padded (45 in this case)
p is the probability of a claim being padded (45% or 0.45 in decimal form)
nCi is the binomial coefficient of n and i, which represents the number of possible combinations of choosing i claims padded out of n total claims.
Now, let's calculate the probability using the formula:
P(X < 45) = ∑(i=0 to 44) (110Ci) * (0.45)^i * (1-0.45)^(110-i)
Calculating this expression will give us the probability.
I'll calculate this probability for you.