Consider the following hypergeometric experiment. Electric fuses produced by Ontario Electric are packaged in boxes of 12 units each. An inspector randomly selects three of the 12 fuses in a box for testing. If the box contains exactly five defective fuses, the probability that the inspector will find exactly one of the three fuses defective is __________. The probability of finding at least 1 defective fuse is __________. NOTE: Write your answers in number format, with 2 decimal places of precision level. Add a leading minus sign symbol, a leading zero and trailing zeros, when needed. Use a period for the decimal separator and a comma to separate groups of thousands.

The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about   40   and a standard deviation of   15 . Suppose that one individual is randomly chosen. Let   X=   percent of fat calories.

In each appropriate box you are to enter either a rational number in "p/q" format or a decimal value accurate to the nearest   0.01 .

1. (.25)   X∼    (pick one) NBUE   (    ,    ) .
   
2. 
   
3. (.25) The probability that a person consumes more than   40   percent fat is    .
   
4. 
   
5. (.25) What is the lowest quartile for percent of fat calorie consumption?    .
   
6. 
   
7. (.25) Write the probability statement for part (c):   P(X  (pick one) ><=   )=  .
   

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A survey conducted for the Northwestern National Life Insurance Company revealed that 70% of American workers say job stress caused frequent health problems. Suppose a random sample of 10 American workers is selected.

What is the probability that more than seven of them say job stress caused frequent health problems?

What is the probability that exactly five say job stress caused frequent health problems?

What is the expected [mean] number of workers that would say job stress caused frequent health problems?

[Hint: Use binomial distribution to answer question]

1. If a seed is planted, it has a 65% chance of growing into a healthy plant. If 12 seeds are planted, what is the probability that exactly 4 don't grow?

2. A manufacturing machine has a 6% defect rate. If 4 items are chosen at random, what is the probability that at least one will have a defect?

3. About 3% of the population has a particular genetic mutation. 500 people are randomly selected.Find the mean for the number of people with the genetic mutation in such groups of 500.

4. When taking a 13 question multiple choice test, where each question has 5 possible answers, it would be unusual to get Incorrect or more questions correct by guessing alone.

From a survey of 120 students attending a university, it was found that 48 were living off campus, 57 were undergraduates, and 25 were undergraduates living off campus. One student is selected at random.
Let event A be “The student is an undergraduate”

Let event B be “The student is living off campus”.

a. Sketch the Venn diagram and show number of students for all parts of the diagram

b. Find the probability that selected person is an undergraduate student or he/she lives off campus

c. Find the probability that selected student is an undergraduate living on campus

d. Selected person is a graduate student living on campus.

With the growing emphasis on technology and the changing business environment, many workers are discovering that training such as re-education, skill development, and personal growth is of great assistance in the job marketplace. A Gallup survey found that 80% of Generation Xers considered the availability of company-sponsored training as a factor to weigh in taking a job. If 50 Generation Xers are randomly sampled, what is the probability that fewer than 35 consider the availability of company-sponsored training as a factor to weigh in taking a job? What is the expected number? What is the probability that between 42 and 47 (inclusive) consider the availability of company-sponsored training as a factor to weigh in taking a job?

A study of the total number of minutes spent in the local emergency room revealed that patients spent on average 162.8 minutes in the ER, with a standard deviation of 53.4 minutes. Assume that the times follow a normal distribution. Let X be the processing time of a randomly selected patient.

(a) Describe the probability distribution of X and state its parameters μ and σ.

(b) Find the probability that the processing time of a randomly selected patient is

i. less than 3 hours.

ii. between 140 and 200 minutes.

iii. more than 2 hours.

(c) Find the 80-th percentile for the processing time of a randomly selected patient.

A prescription drug manufacturer claims that only 10% of all new drugs that are shown to be effective in animal tests ever pass through all the additional testing required to be marketed. The manufacturer currently has eight new drugs that have been shown to be effective in animal tests, and they await further testing and approval. You are not allowed to use PHStat4 for this question. Show your calculations clearly by labeling them properly so that it is clear to infer what the calculations are for

a. Find the probability that none of the drugs is marketed.

b. Find the probability that at least 2 are marketed.

c. Find the expected number of marketed drugs among the eight.

A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 12.9 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 12.9 weeks and that the population standard deviation is 4.8 weeks. Suppose you would like to select a random sample of 99 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 12 and 12.6. P(12 < X < 12.6) =

Find the probability that a sample of size n = 99 is randomly selected with a mean between 12 and 12.6. P(12 < M < 12.6) =

1. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the mean number of customers that pay in cash? Select one:

a. 1.000

b. 0.7

c. 10

d. 7

2. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the standard deviation of the customer that pay in cash?

Select one:

a. 1.000

b. 0.976

c. 0.028

d. 1.449

3. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that at least 9 pay in cash?

Select one:

a. 0.033

b. 0.976

c. 0.024

d. 0.149

4. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that all 10 pay in cash?

Select one:

a. 0.976

b. 0.028

c. 1.000

d. 0.149

5. David's gasoline station offers a discount if the customer pays in cash. Past evidence indicates that 70% of all customers pay in cash (probability of a success). If 10 customers are randomly selected, what is the probability that more than 7 and less than 10 customers pay in cash?

Select one:

a. 0.121

b. 0.354

c. 0.233

d. 0.562