Visit a local retailer/restaurant etc, count number of customers visiting the retailer/restaurant for a period of 10 minutes, count three periods. Use your data, choose appropriate distribution model, help us understand the following questions.

Here is the data

Period 1 = 6 people

Period 2 = 9 people

Period 3 = 7 people

1. What is the probability that there are more than 5 customers showing up within the next 10 minutes?
2. What is the probability that there are more than 10 customers showing up within the next 10 minutes?
3. Validate your findings with the data from the other two 10-minutes slot

Use the following results from a test for marijuana​ use, which is provided by a certain drug testing company. Among 140 subjects with positive test​ results, there are 30 false positive results. Among 152 negative​ results, there are 4 false negative results. Complete parts​ (a) through​ (c). (Hint: Construct a​ table.)

a. How many subjects were included in the​ study?

The total number of subjects in the study was

.b. How many subjects did not use​ marijuana?

A total of subjects did not use marijuana.

c. What is the probability that a randomly selected subject did not use​ marijuana?

The probability that a randomly selected subject did not use marijuana is

5. Nineteen people move out of a neighborhood; four are minorities. Of the nineteen, eight move onto a block with new housing, and one of these eight is a minority. How likely is it that, if there were no discrimination, less than two people out of the eight people on this new block would be minorities? If the resulting probability is less than 0.05, evidence for discrimination exists. Does such evidence exist in this case? (3)

6. There is an average of four accidents per year at a particular intersection.   What is the probability of more than one accident there next month? Hint: Use 1 month = 1/12 of a year to first get the number of accidents that are expected next month.       (3)

Suppose that we have a red coin and a blue coin. The red coin has probability pR = 0.1 of landing heads, and the blue coin has probability pB = 0.2 of landing heads.

(a) Write R code to generate a sequence of coin tosses, starting with the red coin, and switching coins every time a coin lands heads.

(b) Generate 1000 such sequences, each consisting of 1000 coin tosses, and use them to construct a plot of the 2.5%, 50% and 97.5% quantiles of the proportion of red coins tossed as the number of tosses increases. (c) What is the stationary distribution of colours for this process? Comment on how this experiment relates to Birkhoff’s ergodic theorem

A start-up company has 2000 investors, that company loses investors at a rate of 10 per year. Every time the company loses an investor, the company gets a loss of $200,000. For every investor that remains the company makes a profit of $2,000. Let F be the total earnings the company makes in a year, and X be the number of investors the company loses.

1)Write a function that calculates yearly earnings F as a function of X

2)Find P(F < 0), the probability that earnings are negative

3)E[F]

4)What is the probability that the company loses exactly 5 investors in a given year, given that they have not lost any investors in the first half of the year

It is known that 5% of all laptops from a certain manufacturer have a certain defect.A random sample of 20 laptops from this manufacturer is selected.a)What is the probability that no laptops in the sample have defect?.b)What is the probabilty that exactly two laptops in the sample have defect?.c)What is the probabilty that atmost 2 laptops in the sample have the defect?.Let X denote the number of defective laptops in a sample .what is the expected value of X , E[X]?.and Laptops from this manufacturer are sold in batches of 12 and a batch is deemed to be unsatisfactory if it contains 2 or more laptops with defect.If 5 batches are selected at random ,what is the probability that at least 2 of them are deemed unsatisfactory?

1. Class records at Rockwood College indicate that a student selected at random has probability 0.62 of passing French 101. For the student who passes French 101, the probability is 0.81 that he or she will pass French 102. What is the probability that a student selected at random will pass both French 101 and French 102? (Round your answer to three decimal places.)

2. Isabel Briggs Myers was a pioneer in the study of personality types. The personality types are broadly defined according to four main preferences. Do married couples choose similar or different personality types in their mates? The following data give an indication.

Suppose that a married couple is selected at random.

(a) Use the data to estimate the probability that they will have 0, 1, 2, 3, or 4 personality preferences in common. (Enter your answers to 2 decimal places.)

(b) Do the probabilities add up to 1? Why should they?

Yes, because they do not cover the entire sample space.No, because they do not cover the entire sample space.    Yes, because they cover the entire sample space.No, because they cover the entire sample space.

(c ) What is the sample space in this problem?

0, 1, 2, 3 personality preferences in common1, 2, 3, 4 personality preferences in common    0, 1, 2, 3, 4, 5 personality preferences in common0, 1, 2, 3, 4 personality preferences in common

Does the kid factor make a difference? If you are talking photography, the answer may be yes!

Let us say you are a market research person who interviews a random sample of 8 households.

(a) Suppose you interview 8 households with children under the age of 2 years. Let r represent the number of such households that buy film. Make a histogram showing the probability distribution of r for r = 0 through r = 8.

Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)

(b) Suppose that the 8 households are chosen to have no children under 21 years old. Let r represent the number of such households that buy film. Make a histogram showing the probability distribution of r for r = 0 through r = 8.

Find the mean and standard deviation of this probability distribution. (Round your answers to two decimal places.)

(c) Compare the distributions in parts (a) and (b). You are designing TV ads to sell film. Could you justify featuring ads of parents taking pictures of toddlers? Explain your answer.

A Yes. It appears that households with children under 2 are more likely to buy film.

B No. It appears that households with children under 2 are more likely to buy film.

C No. It appears that households with no children under 21 are more likely to buy film.

D Yes. It appears that households with no children under 21 are more likely to buy film.

2)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 132000 dollars. Assume the standard deviation is 31000 dollars. Suppose you take a simple random sample of 59 graduates.

Find the probability that a single randomly selected salary has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < X < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=59n=59 has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < ¯xx¯ < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

3)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.1 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.1 weeks and that the population standard deviation is 5.4 weeks. Suppose you would like to select a random sample of 91 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35 and 37.2.
P(35 < X < 37.2) =

Find the probability that a sample of size n=91n=91 is randomly selected with a mean between 35 and 37.2.
P(35 < ¯xx¯ < 37.2) =

Enter your answers as numbers accurate to 4 decimal places.

4)CNNBC recently reported that the mean annual cost of auto insurance is 957 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 73 auto insurance policies. (Do not use tables unless directed to do so.)

Find the probability that a single randomly selected value is more than 994 dollars.
P(X > 994) =

Find the probability that a sample of size n=73n=73 is randomly selected with a mean that is more than 994 dollars.
P(¯xx¯ > 994) =

Enter your answers as numbers accurate to 4 decimal places.

5)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 168000 dollars. Assume the standard deviation is 43000 dollars. Suppose you take a simple random sample of 70 graduates.

Do not use probability tables to find the probabilities below as they may not be accurate enough.

Find the probability that a single randomly selected salary is more than 164000 dollars.
P(X > 164000) =

Find the probability that a sample of size n=70n=70 is randomly selected with a mean that is more than 164000 dollars.
P(¯xx¯ > 164000) =

Enter your answers as numbers accurate to 4 decimal places.

6)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 9 weeks. Suppose you would like to select a random sample of 38 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 24.
P(X < 24) =

Find the probability that a sample of size n=38n=38 is randomly selected with a mean less than 24.
P(¯xx¯ < 24) =

Enter your answers as numbers accurate to 4 decimal places.

7)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 261.5-cm and a standard deviation of 0.5-cm. For shipment, 13 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 261.7-cm.
P(¯xx¯ < 261.7-cm) =

Enter your answer as a number accurate to 4 decimal places.

2)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 132000 dollars. Assume the standard deviation is 31000 dollars. Suppose you take a simple random sample of 59 graduates.

Find the probability that a single randomly selected salary has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < X < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

Find the probability that a random sample of size n=59n=59 has a mean value between 116260.2 and 145318.3 dollars.
P(116260.2 < ¯xx¯ < 145318.3) =  (Enter your answers as numbers accurate to 4 decimal places.)

3)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 36.1 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 36.1 weeks and that the population standard deviation is 5.4 weeks. Suppose you would like to select a random sample of 91 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is between 35 and 37.2.
P(35 < X < 37.2) =

Find the probability that a sample of size n=91n=91 is randomly selected with a mean between 35 and 37.2.
P(35 < ¯xx¯ < 37.2) =

Enter your answers as numbers accurate to 4 decimal places.

4)CNNBC recently reported that the mean annual cost of auto insurance is 957 dollars. Assume the standard deviation is 271 dollars. You take a simple random sample of 73 auto insurance policies. (Do not use tables unless directed to do so.)

Find the probability that a single randomly selected value is more than 994 dollars.
P(X > 994) =

Find the probability that a sample of size n=73n=73 is randomly selected with a mean that is more than 994 dollars.
P(¯xx¯ > 994) =

Enter your answers as numbers accurate to 4 decimal places.

5)Business Weekly conducted a survey of graduates from 30 top MBA programs. On the basis of the survey, assume the mean annual salary for graduates 10 years after graduation is 168000 dollars. Assume the standard deviation is 43000 dollars. Suppose you take a simple random sample of 70 graduates.

Do not use probability tables to find the probabilities below as they may not be accurate enough.

Find the probability that a single randomly selected salary is more than 164000 dollars.
P(X > 164000) =

Find the probability that a sample of size n=70n=70 is randomly selected with a mean that is more than 164000 dollars.
P(¯xx¯ > 164000) =

Enter your answers as numbers accurate to 4 decimal places.

6)A leading magazine (like Barron's) reported at one time that the average number of weeks an individual is unemployed is 23 weeks. Assume that for the population of all unemployed individuals the population mean length of unemployment is 23 weeks and that the population standard deviation is 9 weeks. Suppose you would like to select a random sample of 38 unemployed individuals for a follow-up study.

Find the probability that a single randomly selected value is less than 24.
P(X < 24) =

Find the probability that a sample of size n=38n=38 is randomly selected with a mean less than 24.
P(¯xx¯ < 24) =

Enter your answers as numbers accurate to 4 decimal places.

7)A company produces steel rods. The lengths of the steel rods are normally distributed with a mean of 261.5-cm and a standard deviation of 0.5-cm. For shipment, 13 steel rods are bundled together.

Find the probability that the average length of a randomly selected bundle of steel rods is less than 261.7-cm.
P(¯xx¯ < 261.7-cm) =

Enter your answer as a number accurate to 4 decimal places.