A person’s blood glucose level and diabetes are closely related. Let X be a random variable measured in milligrams of glucose per deciliter (1/10 of a liter) of blood. Suppose that after a 12-hour fast, the random variable X will have a distribution that is approximately normal with mean µ = 90 and standard deviation σ = 20. (Round your answers to three decimal places.)

(A) (3 points) What is the probability that X is greater than 90? (B) (3 points) What is the probability that X is between 70 and 110? (C) (3 points) What is the probability that X is between 55 and 100? (D) (3 points) What is the probability that X is less than 50 or greater than 90? (E) (3 points) What is the probability that X is less than 85?

a. Consider the following distribution of a random variable X

                Find the mean, variance and standard deviation

b. There are 6 Republican, 5 Democrat, and 4 Independent candidates. Find the probability the committee will be made of 3 Republicans, 2 Democrats, and 2 Independent be selected?

c. At a large university, the probability that a student takes calculus and is on the dean’s list is 0.042. The probability that a student is on the dean’s list is 0.21. Find the probability that the student is taking calculus given that the student is on the dean’s list.

d. In a statistics class there are 16 juniors and 12 seniors; 8 of the senior students are females, and 12 of the juniors are males. If a student is selected at random, find the probability that the student is neither a junior nor a male.

3. Consider the following system made up of functional components in parallel and series.

3-1. (2 points) What is the probability that the system operates? Answer: .  

3-2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. Answer: .

3-3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. Answer: .  

3-4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.99 and when the probability that component C3 functions is improved to a value of 0.99. Which improvement increases the system reliability more?

According to national data, 20.7% of burglaries are cleared with arrests. A new detective is assigned to six different burglaries. What is the probability that at least one of them is cleared with an arrest?

Consider 4 species of plants in Point of Rocks Park where there are 160 White Pines, 80 Hackberries, 300 Pin Oaks, and 60 Tulip Poplars. What is the probability, and explain how you go about finding the probability, of randomly picking a Pin Oak out of this park.

The probability is . To get the probability, divide  by .

Dr. Baum is analyzing the distribution of two genus of trees, Acer and Quercus.  In the forest you are currently studying with her, there are 11 species in the genus Acer, while there are 87 species of the genus Quercus. How many possible combinations, consisting of one member from each genus, are possible?

When an opinion poll calls landline telephone numbers at random, approximately 30% of the numbers are working residential phone numbers. The remainder are either non-residential, non-working, or computer/fax numbers. You watch the random dialing machine make 20 calls. (Round your answers to four decimal places.)

(a) What is the probability that exactly 4 calls reach working residential numbers?


(b) What is the probability that at most 4 calls reach working residential numbers?


(c) What is the probability that at least 4 calls reach working residential numbers?


(d) What is the probability that fewer than 4 calls reach working residential numbers?


(e) What is the probability that more than 4 calls reach working residential numbers?

According to a poll on consumer​ behavior, 36​% of people say they will only consider cars manufactured in their country when purchasing a new car. Suppose you select a random sample of 100 respondents. Complete parts​ (a) through​ (c) below.

a. What is the probability that the sample will have between 35​% and 45​% who say they will consider only cars manufactured by a company in their country when purchasing a new​ car? The probability is 0.5521. ​(Round to four decimal places as​ needed.)

b. The probability is 80​% that the sample will be contained within what symmetrical limits of the population​ percentage? The probability is 80​% that the sample percentage will be contained above 29.8​% and below 42.2​%. ​(Round to one decimal place as​ needed.)

c. The probability is 68​% that the sample will be contained within what symmetrical limits of the population​ percentage? The probability is 68​% that the sample percentage will be contained above 31.2​% and below 40.8​%. ​(Round to one decimal place as​ needed.)

How to solve in excel I already have answers but dont know how to do on excel.

Before 1918, approximately 60% of the wolves in the New Mexico and Arizona region were male, and 40% were female. However, cattle ranchers in this area have made a determined effort to exterminate wolves. From 1918 to the present, approximately 65% of wolves in the region are male, and 35% are female. Biologists suspect that male wolves are more likely than females to return to an area where the population has been greatly reduced. (Round your answers to three decimal places.)

(a) Before 1918, in a random sample of 11 wolves spotted in the region, what is the probability that 8 or more were male?


What is the probability that 8 or more were female?


What is the probability that fewer than 5 were female?


(b) For the period from 1918 to the present, in a random sample of 11 wolves spotted in the region, what is the probability that 8 or more were male?


What is the probability that 8 or more were female?


What is the probability that fewer than 5 were female?

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 49 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.3 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 60 pounds
b. More than 56 pounds
c. Between 55 and 57 pounds
d. Less than 55 pounds
e. Less than 48 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 60 pounds

b. enter the probability that the sample mean will be more than 56 pounds

c. enter the probability that the sample mean will be between 55 and 57 pounds

d. enter the probability that the sample mean will be less than 55 pounds

e. enter the probability that the sample mean will be less than 48 pounds

The Aluminum Association reports that the average American uses 56.8 pounds of aluminum in a year. A random sample of 50 households is monitored for one year to determine aluminum usage. If the population standard deviation of annual usage is 12.2 pounds, what is the probability that the sample mean will be each of the following?

Appendix A Statistical Tables

a. More than 58 pounds
b. More than 57 pounds
c. Between 56 and 58 pounds
d. Less than 55 pounds
e. Less than 49 pounds

(Round the values of z to 2 decimal places. Round your answers to 4 decimal places.)

a. enter the probability that the sample mean will be more than 58 pounds

b. enter the probability that the sample mean will be more than 57 pounds

c. enter the probability that the sample mean will be between 56 and 58 pounds

d. enter the probability that the sample mean will be less than 55 pounds

e. enter the probability that the sample mean will be less than 49 pounds

The following table is a summary of one of the key questions in the employee satisfaction survey for XYZ Limited. If an employee (a male) is randomly selected, answer the questions below: (14 points)   

1. What is the probability that he is from the Uptown branch?
2. What is the probability that he plans to be with the company one year from now?
3. What is the probability that he is from the Downtown branch and plan to be with the company one year from now?
4. What is the probability that he is from the Uptown branch or does not plan to be with the company one year from now?
5. What is the probability that he is from the Downtown branch if he plans to be with the company one year from now?
6. What is the probability that he plans to be with the company one year from now given that he is from the Uptown branch?
7. Are the events “Downtown Branch” and “plans to be with the company one year from now” independent? Justify your answer using probabilities.