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 a binomial probability distribution.
In this case, we have 110 insurance claims and the probability of each claim being padded is 0.45. We want to find the probability of having fewer than 45 claims padded.
To get the answer, we can use a binomial probability formula, which is:
P(X < k) = sum of P(X = i), where i ranges from 0 to k-1
In this case, k is 45.
Now, we can calculate the probability using this formula:
P(X < 45) = sum of P(X = i), where i ranges from 0 to 44
Using a binomial probability calculator or a statistical software, we can find the sum of these probabilities to get the final answer:
P(X < 45) = 0.8059
So, the probability that fewer than 45 of the claims have been padded is approximately 0.806.