) A bank's loan officer randomly selects an applicant's credit rating. The credit ratings are normally distributed with a mean of 110 and a standard deviation of 25. a) Find the probability that the applicant's credit rating is less than 135.

b) Find the probability that the applicant's credit rating is greater than 100.

c) Find the probability that the applicant's credit rating is between 60 and 160.

A production lot of 80 units has 8 defective items. We draw a random sample of 10 units and we want to know:
a.- the probability that the sample contains less than 3 defective articles
b.- the probability that the sample contains at least 3 good articles
c.- the probability that the sample contains more than 6 good articles

1. What is the fair price that must be paid to enter a game in which you can win $ 950 with 0.1 of probability, $ 2.5 with 0.4 probability and lose $ 14 with 0.5 probability?

2. A person throws 2 dice and receives the sum of the results obtained in pesos, how much must he pay per game to have a fair game?

According to the Bureau of Labor Statistics, the annual wage for a federal employee in 2017 was $76,250. Assume the population standard deviation is $28,025. A random sample of 34 federal employees is selected.

1. What is the probability that the sample mean will be less than $70,000?
2. What is the probability that the sample mean will be more than $74,000?
3. What is the probability that the sample mean will be between $76,000 and $81,000.

3. An urn contains 12 red balls and 8 green balls. Six balls are drawn randomly with replacement

a. Find the probability of drawing exactly two red balls?

b. Find the probability of drawing at least one green ball?

c. Find the probability of drawing exactly two green balls when the drawings are done without replacement?

You have thoroughly mixed 10 million cells in 10 mL of tissue culture medium to be plated in 96 wells of a microliter plates, delivering 100 microliters per well.

a. What is the probability that a well will have no cells in it?

b. What is the probability that a well have one cell?

c. What is the probability that a well will have 3 cells or more?

As per the records, the data of subjects with Alzheimer’s disease roughly follow normal distribution with

mean age of 80 years and standard deviation 16 years.

a. What is the probability that a subjects’ age is between 63 and 78 years?

b. What is the probability that a subjects’ age is between 74 and 97?

c. What is the probability that a subjects’ age is less than 80?

1. There are 50 reports to be read. Ten are to be chosen for today’s work.
2. 1. How many different possibilities are there for choosing the reports?
   2. If 5 of the 50 reports are important, what is the probability that at least 1 important report is read?
   3. What is the probability of no more than 1 important report to be read?
   4. Using the previous two results, what is the probability of exactly 1 report being read?