The Brooklyn District Attorney's office analyzed the leading (leftmost) digits of check amounts in order to identify fraud. The leading digit of 1 is expected to occur 30.1% of the time, according to "Benford's law," which applies in this case. Among 784 checks issued by a suspect company, there were none with amounts that had a leading digit of 1. If there is a 30.1% chance that the leading digit of the check amount is 1, what is the expected number of checks among 784 that should have a leading digit of 1

The expected number of checks among 784 that should have a leading digit of "1" is 236.

Step-by-step explanation:

Let X = number of checks that has the leading digit as "1".

The probability of a check having a leading digit as "1" is, p = 0.301.

The number of checks issued by a suspected company is, n = 784.

A check is having a leading digit "1" is independent of other checks.

A randomly selected check either has the leading digit 1 or not.

The success of the experiment is defined as, a check having the digit "1" as the leading digit.

The random variable X follows a Binomial distribution with parameters n = 784 and p = 0.301.

The expected value of a random variable is the average number of times the random variable occurs.

The formula to compute the expected value of a Binomial distribution is:

Compute the expected value of X as follows:

Thus, the expected number of checks among 784 that should have a leading digit of "1" is 236.

for the points! : )

8

step-by-step explanation:

to find the amount of gift bags to use all the supplies, find the gcf or greatest common factor. this is the largest number which multiplies evenly into each term.

48 has factors: 1, 2, 3, 4, 6, 8, 12. 16, 24, 48

80 has factors: 1, 2, 4, 5, 8, 10, 16, 20, 40, 80

64 has factors: 1, 2, 4, 8, 8, 16, 32, 64

the highest number factor they all share in common is 8. this means there will be 8 bags with 6 pencils, 10 markers, and 8 stickers in each bag.