According to the book Are you Normal?,40% of all US adults try to pad their auto insurance claims to cover their deductible. Your office has just received 128 in insurance claims to be processed in the next few days, what is the probability that fewer than 45 of the claims have been padded? Round your answer to the nearest thousandths place.

Use the normal approximation to the binomial distribution.

Mean = np = 128 * .40 = 51.2
Standard deviation = √npq = √(128 * .40 * .60) = √30.72 = 5.54

Note: q = 1 - p

Formula for z-scores:
z = (x - mean)/sd

With your data:
z = (45 - 51.2)/5.54 = -1.12

Look at a z-table for the probability using the z-score.

Double check my calculations.

I hope this will help.

the answer is 0.113 its confusing and i got it wrong the first time too, (same class)

To solve this problem, we need to use the binomial probability formula. The formula for the probability of getting exactly k successes in n trials, when the probability of success is p, is given by:

P(k) = (n C k) * p^k * (1-p)^(n-k)

In this case, we want to find the probability of getting fewer than 45 padded claims out of 128 claims. Since the probability of padding a claim is given as 40%, or 0.40, the probability of not padding a claim is 1 - 0.40 = 0.60.

Let's calculate the probability of getting exactly 45 padded claims and subtract it from 1 to get the probability of getting fewer than 45 padded claims.

P(fewer than 45 padded claims) = 1 - P(exactly 45 padded claims)

P(exactly 45 padded claims) = (128 C 45) * (0.40)^45 * (0.60)^(128-45)

To calculate (n C k), we use the combination formula: (n C k) = n! / (k! * (n-k)!), where "!" denotes factorial.

Calculating the values:

(128 C 45) = 128! / (45! * (128-45)!)
= 128! / (45! * 83!)

(0.40)^45 = 0.40^45

(0.60)^(128-45) = 0.60^83

Now, let's calculate P(fewer than 45 padded claims):
P(fewer than 45 padded claims) = 1 - P(exactly 45 padded claims)
P(fewer than 45 padded claims) = 1 - [(128! / (45! * 83!)) * (0.40^45) * (0.60^83)]

Calculating the expression will give you the probability of having fewer than 45 padded claims out of 128 claims.