1. A pipeline is to be inspected. There is a 10% chance that any 100ft section of pipeline will contain at least one defect (thinning walls, weld defect, etc). Assume the sections are independent (whether one sections fails or not is independent of whether other sections fail or not).
   1. What is the probability that, given 2 defective sections have been found so far, that exactly 12 sections of pipeline have been inspected?
   2. What is the probability that, given 50 sections have been inspected so far, that fewer than 5 defective sections have been found?
   3. What is the probability that the first defect will be found in the 10^th pipeline inspected?
   4. What is the average (expected) number of defects per 100 pipelines sections inspected?
   5. Comment on the independence assumption. Do you believe this is a realistic assumption for a pipeline? Why or why not?

The ACT is a college entrance exam. ACT test scores follow a normal distribution with a mean of 22.2 points and a standard deviation of 4.9 points. Let X = number of points scored on the ACT. Answer the following questions.

A. Jasmine scored a 28.227 on the ACT. Calculate Jasmine's Z-score.

B. Interpret Jasmine's z-score in terms of the problem.

C. What is the probability that a randomly selected individual gets an ACT score that is lower than Jasmine's? Round your answer to four decimal places.

D. What is the probability that a randomly selected individual gets a score greater than Jasmine's? Round answers to four decimal places.

E. What is the probability that a randomly selected individual scores between 18.378 and 28.864 points? Round answers to four decimal places.

1.A person who unknowingly carries a communicable disease arrives at a crowded partyat which 45 other people are present. Studies have shown that typically 4% of those at the party will become infected.

a)What is the probability that 2 or more of those at the party will also become infected?

b)Justify an appropriate approximate method for finding the probability in a); carry it out, and compare your two answers.

2.A large animal preserve has noticed that an albino panther is born unpredictably once every 8 years; and that can happen at any time of the year.

a) What are the expected value and variance of the number of albino panthers which will be born in the next 40 years?

b) What is the probability the preserve will go 10 years without having another albino panther born?

You may need to use the appropriate appendix table or technology to answer this question.

After deducting grants based on need, the average cost to attend the University of Southern California (USC) is $27,175. Assume the population standard deviation is $7,400. Suppose that a random sample of 54 USC students will be taken from this population.

(a)

What is the value of the standard error of the mean? (Round your answer to the nearest whole number.)

$

(b)

What is the probability that the sample mean will be more than $27,175?

(c)

What is the probability that the sample mean will be within $1,000 of the population mean? (Round your answer to four decimal places.)

(d)

What is the probability that the sample mean will be within $1,000 of the population mean if the sample size were increased to 100? (Round your answer to four decimal places.)

1. A university found that 10% of students withdraw from a math course. Assume 25 students are enrolled.
   1. Write the prob. distribution function with the specific parameters for this problem

1. 2. Compute by hand (can use calculator but show some work) the pro that exactly 2 withdraw.
2. 3. Compute by hand (can use calculator but show some work) the prob. that exactly 5 withdraw.
3. 4. Construct the probability distribution table of class withdrawals in Excel. This is a table of x and f(x). Generate one column for the number of x successes with numbers 0 to 25 in each row. Generate a second column with the probability f(x) of each success using the Excel function =BINOM.DIST(x, n, p, FALSE) in each row. Attach the table
4. 5. What is the probability that 5 or less will withdraw?

•Exercise 1: It is assumed that 80% of the students pass the MBA 510 course. Calculate the following for a class of 15 students:

(a) the mean number of students expected to pass;

(b) the standard deviation;

(c) P(exactly 12 of the 15 students pass);

(d) P(at least 12 of the 15 students pass).

•Exercise 2: Five customers enter a store and make independent purchase decisions. The store’s records indicate that 20% of all customers who enter the store will make a purchase.         

(a) Does a general discrete probability distribution or the binomial distribution apply?

(b) Write the probability form applicable.  

Calculate the probability that:

(c) exactly 4 customers will make a purchase;

(d) less than 3 customers will make a purchase.

Please show all the work in Excel or Word.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.893 g and a standard deviation of 0.306 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 44 cigarettes with a mean nicotine amount of 0.819 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly selecting 44 cigarettes with a mean of 0.819 g or less.
P(M < 0.819 g) = _________
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.962 g and a standard deviation of 0.313 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 48 cigarettes with a mean nicotine amount of 0.899 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 48 cigarettes with a mean of 0.899 g or less.  
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough (greater than a 5% chance) to have been a chance occurrence.
• Yes. The probability of this data is unlikely (less than a 5% chance) to have occurred by chance alone.

The amounts of nicotine in a certain brand of cigarette are normally distributed with a mean of 0.908 g and a standard deviation of 0.319 g. The company that produces these cigarettes claims that it has now reduced the amount of nicotine. The supporting evidence consists of a sample of 46 cigarettes with a mean nicotine amount of 0.856 g.

Assuming that the given mean and standard deviation have NOT changed, find the probability of randomly seleting 46 cigarettes with a mean of 0.856 g or less.
P(x-bar < 0.856 g) =
Enter your answer as a number accurate to 4 decimal places.

Based on the result above, is it valid to claim that the amount of nicotine is lower?

• No. The probability of obtaining this data is high enough to have been a chance occurrence.
• Yes. The probability of this data is unlikely to have occurred by chance alone.

4. Customers enter a store at a rate of 3 customers per hour.

a) Compute the probability that at least two, but no more than five customers enter the store in a given hour.

b) Compute the probability that it takes more than 30 minutes for the first customer to enter the store this hour.

c) Suppose you know that exactly 1 customer entered the store during a given hour. Compute the probability that the customer entered the store between minute 10 and minute 30.

d) Let Xk be the number of customers that enter a store during hour k. Suppose you recorded how many customers entered the store each hour for the last 60 hours. What is the approximate distribution of X¯? Make sure to specify the parameter(s) of the distribution.