problem is also a Monte Carlo simulation, but this time in the continuous domain: must use the following fact: a circle inscribed in a unit square

has as radius of 0.5 and an area of ?∗(0.52)=?4.π∗(0.52)=π4.

Therefore, if you generate num_trials random points in the unit square, and count how many land inside the circle, you can calculate an approximation of ?

For this problem, you must create code in python

(A) Draw the diagram of the unit square with inscribed circle and 500 random points, and calculate the value of ?

(B) Without drawing the diagram, calculate the value of ? you would get from 10⁵ trials.

(C) After completing (B), try to get a more accurate value for ? by increasing the number of trials.The results will depend on your machine

Grooming Time.   Listed below are times (minutes) spent on hygiene and grooming in the morning (by randomly selected subjects) (based on data from a Svenska Cellulosa Aktiebolager survey). TAKEN FROM Elementary Statistics 13th ED. BY  Mario F Triola; CHPT 2

Data: 0   5   20 22   24   25   25   25   27   27   28   30   30   35   35   40   45

1. To construct a frequency distribution with 6 classes, describe how you determine the class width.
2. If you want to have 6 classes for the data above, what would the class width be? Show work illustrating how you determined the class width.
3. Using lower and upper class limits, list all six classes in increasing order.
4. Construct the frequency distribution by determining and listing the corresponding frequency for each class.
5. Construct the relative frequency distribution. Using the first class as an example, show how you are determining relative frequency.
6. Construct the cumulative frequency distribution.

Researchers collected data to examine the relationship between pollutants and preterm births in Southern California. During the study air pollution levels were measured by air quality monitoring stations. Specifically, levels of carbon monoxide were recorded in parts per million, nitrogen dioxide and ozone in parts per hundred million, and coarse particulate matter PM₁₀ in μμg/m3. Length of gestation data were collected on 143,196 births between the years 1989 and 1993, and air pollution exposure during gestation was calculated for each birth. The analysis suggested that increased ambient PM₁₀ and, to a lesser degree, CO concentrations may be associated with the occurrence of preterm births.

a. The paragraph above describes an

A. Observational Study
B. Experiment

b. The cases in this research are

A. Each year between 1989 and 1993
B. Each type of pollution measured by air quality monitoring stations
C. Each birth between 1989 and 1993
D. Air pollution exposure during gestation

c. What is the research question?

A. How can expectant mothers avoid air pollution?
B. How much air pollution is there in Southern California?
C. How prevalent was preterm birth during the years 1989 to 1993?
D. Are preterm births associated with air pollution levels?

d. What is the population of interest?

A. All air quality monitoring stations
B. All years for which air quality has been measured
C. All human babies
D. All environmental pollutants

e. What is the sample?

A. The 143,196 births
B. All air quality monitoring stations
C. The pollution measurements for the 4 pollutants
D. The years between 1989 and 1993

f. Can the findings of this study be used to establish casual relationships?

A. No, because this is an observational study
B. Yes, because air pollution is bad for human health
C. No, because this is an experiment
D. Yes, because the sample size is so large

need help no clue what i am doing wrong?

The blood platelet counts of a group of women have a​ bell-shaped distribution with a mean of 261.7 and a standard deviation of 65.5. ​(All units are 1000 ​cells/mu​L.) Using the empirical​ rule, find each approximate percentage below. a. What is the approximate percentage of women with platelet counts within 2 standard deviations of the​ mean, or between 130.7 and 392.7​? b. What is the approximate percentage of women with platelet counts between 65.2 and 458.2​?

For each measurement listed below replace the “?” with the most appropriate level or scale of measurement: nominal, ordinal, interval, ratio.

I have figured them all out except D

On average, commuters in Phoenix, Arizona, area require m= 40.0 minutes to get to work.  Assume the times to get to work are normallydistributed with a standard deviation of s= 10 minutes, and that Joe is an average Phoenix resident.

1. What is the probability that on any given day Joe will require over 45 minutes to get to work?

2. What is the probability it will take Joe exactly40.0 minutes to get to work on any given day?

3. Joe has just left home from lunch to attend a meeting with the CEO in 30 minutes.  If the CEO routinely fires employees who are tardy for meetings, what is the probability the Joe will still be employed tomorrow?

4. Joe leaves home for work at exactly the same time.  His work starts at 8:00 AM sharp.  Due to traffic jams during the morning rush hour, Joe was tardy for work on 38.2% of the time.  What time does Joe leave home for work every morning?  Briefly explain your train of thought in arriving to the answer.

Assume that the two samples are from a normal population. Please perform a t test for the differences in sample averages, indicating whether it is significant to 95% confidence (0.05 significance) using one and/or two sided. Assume that the population standard deviation is unknown but presumed equal. Show one-sided and two-sided actual Probability and Critical values using hand calculations and Excel

A 25 24 15 20 21 23 25 28 35 34

B 15 11 14 23 24 20 22 24 25 22

A) Fill in the blanks. According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.07 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 332 independent returns from this year, around __________ returns, give or take __________, will be fraudulent or will contain errors that are purposely made to cheat the IRS.

B)

According to estimates by the office of the Treasury Inspector General of IRS, approximately 0.0354 of the tax returns filed are fraudulent or will contain errors that are purposely made to cheat the IRS. In a random sample of 393 independent returns from this year, what is the probability that greater than 10 will be fraudulent or will contain errors that are purposely made to cheat the IRS?

C)

Suppose that the probability of a baseball player getting a hit in an at-bat is 0.2884. If the player has 40 at-bats during a week, what's the probability that he gets exactly 16 hits?

Problem 10-07 (Algorithmic)

Aggie Power Generation supplies electrical power to residential customers for many U.S. cities. Its main power generation plants are located in Los Angeles, Tulsa, and Seattle. The following table shows Aggie Power Generation's major residential markets, the annual demand in each market (in megawatts or MWs), and the cost to supply electricity to each market from each power generation plant (prices are in $/MW).

1. If there are no restrictions on the amount of power that can be supplied by any of the power plants, what is the optimal solution to this problem? Which cities should be supplied by which power plants? What is the total annual power distribution cost for this solution? If required, round your answers to two decimal places.
   
   The optimal solution is to produce  MWs in Los Angeles,  MWs in Tulsa, and  MWs in Seattle. The total distribution cost of this solution is $  .
   
2. If at most 3800 MWs of power can be supplied by any one of the power plants, what is the optimal solution? What is the annual increase in power distribution cost that results from adding these constraints to the original formulation? If required, round your answers to two decimal places.
   
   What is the optimal solution to produce ____ MWs in Los Angeles?
3. What is the optimal solution to produce ____ MWs in Tulsa?
4. What is the optimal solution to produce ____ MWs in Seattle?
5. What is the total distribution cost of this solution?
6. What is the increase in cost associated with the additional constraints?

To obtain information on the corrosion-resistance properties of a certain type of steel conduit, 45 specimens are buried in soil for a 2-year period. The maximum penetration (in mils) for each specimen is then measured, yielding a sample average penetration of x = 52.4 and a sample standard deviation of s = 4.5. The conduits were manufactured with the specification that true average penetration be at most 50 mils. They will be used unless it can be demonstrated conclusively that the specification has not been met. What would you conclude? (Use α = 0.05.)
State the appropriate null and alternative hypotheses.

A- H₀: μ ≠ 50
H_a: μ > 50

B-) H₀: μ = 50
H_a: μ ≠ 50

C-) H₀: μ = 50
H_a: μ > 50

D-) H₀: μ > 50
H_a: μ = 50

Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to four decimal places.)

State the conclusion in the problem context.

Reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils.

Do not reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils.    

Do not reject the null hypothesis. There is not sufficient evidence to conclude that the true average penetration is more than 50 mils.

Reject the null hypothesis. There is sufficient evidence to conclude that the true average penetration is more than 50 mils.

Roll two dice at the same time, and define a random variable X as the sum of the two faces observed. Determine the CDF and PMF of X. Sketch the CDF.

Is the national crime rate really going down? Some sociologists say yes! They say that the reason for the decline in crime rates in the 1980s and 1990s is demographics. It seems that the population is aging, and older people commit fewer crimes. According to the FBI and the Justice Department, 70% of all arrests are of males aged 15 to 34 years.† Suppose you are a sociologist in Rock Springs, Wyoming, and a random sample of police files showed that of 31 arrests last month, 23 were of males aged 15 to 34 years. Use a 1% level of significance to test the claim that the population proportion of such arrests is the city different from 70%. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p̂ is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two decimal places. Round the P-value to four decimal places.)

State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.There is insufficient evidence at the 0.01 level to conclude that the true proportion of such arrests in the city differs from 70%.    

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.    The conclusions obtained by using both methods are the same.

A) If the statistical test performed on the data gives p = 0.001 in the case where the alternative hypothesis H1 is true, the resulting conclusion is (at 5% significance level)

Choose one:
1. right negative
2. false negative
3. right positive
4. false positive
5. True, but it is not known whether it is positive or negative
6. False, but it is not known whether it is positive or negative
7. positive, but it is not known whether it is right or wrong
8. negative, but it is not known whether it is right or wrong.

B) If the statistical test performed on the data gives p = 0.6 in the case where the null hypothesis H0 is true, the resulting conclusion is (at 5% significance level)

Choose one:
1. right negative
2. false negative
3. right positive
4. false positive
5. True, but it is not known whether it is positive or negative
6. False, but it is not known whether it is positive or negative
7. positive, but it is not known whether it is right or wrong
8. negative, but it is not known whether it is right or wrong.

C) If the statistical test performed on the data gives p = 0.003 in the case where the null hypothesis H0 is true, the resulting conclusion is (at 5% significance level)

Choose one:
1. right negative
2. false negative
3. right positive
4. false positive
5. True, but it is not known whether it is positive or negative
6. False, but it is not known whether it is positive or negative
7. positive, but it is not known whether it is right or wrong
8. negative, but it is not known whether it is right or wrong.

D) If the statistical test performed on the data gives p = 0.4 in the case where the null hypothesis H0 is false, the resulting conclusion is (at 5% significance level)

Choose one:
1. right negative
2. false negative
3. right positive
4. false positive
5. True, but it is not known whether it is positive or negative
6. False, but it is not known whether it is positive or negative
7. positive, but it is not known whether it is right or wrong
8. negative, but it is not known whether it is right or wrong.

Thank you so much if anyone can help me! I would need only the answers :)

The U.S. Department of Transportation, National Highway Traffic Safety Administration, reported that 77% of all fatally injured automobile drivers were intoxicated. A random sample of 33 records of automobile driver fatalities in Kit Carson County, Colorado, showed that 18 involved an intoxicated driver. Do these data indicate that the population proportion of driver fatalities related to alcohol is less than 77% in Kit Carson County? Use α = 0.01. Solve the problem using both the traditional method and the P-value method. Since the sampling distribution of p̂ is the normal distribution, you can use critical values from the standard normal distribution as shown in the table of critical values of the z distribution. (Round the test statistic and the critical value to two decimal places. Round the P-value to four decimal places.)

State your conclusion in the context of the application.

There is sufficient evidence at the 0.01 level to conclude that the true proportion of driver fatalities related to alcohol is less than 77%.There is insufficient evidence at the 0.01 level to conclude that the true proportion of driver fatalities related to alcohol is less than 77%.    

Compare your conclusion with the conclusion obtained by using the P-value method. Are they the same?

We reject the null hypothesis using the P-value method, but fail to reject using the traditional method.The conclusions obtained by using both methods are the same.    We reject the null hypothesis using the traditional method, but fail to reject using the P-value method.