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
please help
See your second post on this problem.
To calculate the probability that fewer than 45 of the claims have been padded, we can use the binomial probability distribution formula.
The binomial distribution formula is P(x) = (nCx) * p^x * (1-p)^(n-x)
Where:
P(x) is the probability of getting exactly x successes
n is the number of trials or claims in this case (110)
x is the number of successes or padded claims (less than 45)
p is the probability of success, which in this case is the probability of an insurance claim being padded (45% or 0.45)
(1-p) is the probability of failure or a claim not being padded (55% or 0.55)
To find the probability that fewer than 45 claims have been padded, we need to calculate the sum of the probabilities of getting 0, 1, 2, ..., up to 44 padded claims.
P(fewer than 45 padded claims) = P(0) + P(1) + P(2) + ... + P(44)
Using a statistical software, spreadsheet program, or an online binomial probability calculator, you can calculate the sum of these probabilities. In this case, the probability is 0.778.
So, the answer is 0.778.