Suppose that the probability function in the table below reflects the possible lifetimes (in months after emergence) for fruit flies. Let the random variable X measure fruit fly lifetimes (in months).

Fruit fly lifetimes (in months)

(a) What proportion of fruit flies die in their second month? P(x=2)

(b) What is the probability that a fruit fly lives more than four months?
(c) What is the mean lifetime for a fruit fly?
(d) What is the standard deviation of fruit fly lifetimes?

Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the​ P-value method or the traditional method of testing hypotheses. Company A uses a new production method to manufacture aircraft altimeters. A simple random sample of new altimeters resulted in errors listed below. Use a 0.05 level of significance to test the claim that the new production method has errors with a standard deviation greater than 32.2​ ft, which was the standard deviation for the old production method. If it appears that the standard deviation is​ greater, does the new production method appear to be better or worse than the old​ method? Should the company take any​ action? negative 42​, 78​, -25​, -70​, -43​, 10​, 15​, 54​, -9​,-50​, -106​, -106

For this problem, carry at least four digits after the decimal in your calculations. Answers may vary slightly due to rounding.

In a random sample of 70 professional actors, it was found that 42 were extroverts.

(a)

Let p represent the proportion of all actors who are extroverts. Find a point estimate for p. (Round your answer to four decimal places.)
1

(b)

Find a 95% confidence interval for p. (Round your answers to two decimal places.)
lower limit         2
upper limit         3

Give a brief interpretation of the meaning of the confidence interval you have found.

We are 95% confident that the true proportion of actors who are extroverts falls outside this interval. We are 5% confident that the true proportion of actors who are extroverts falls within this interval.     We are 5% confident that the true proportion of actors who are extroverts falls above this interval. We are 95% confident that the true proportion of actors who are extroverts falls within this interval.

(c)

Do you think the conditions n·p > 5 and n·q > 5 are satisfied in this problem? Explain why this would be an important consideration.

Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately binomial. No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately binomial.     No, the conditions are not satisfied. This is important because it allows us to say that p̂ is approximately normal. Yes, the conditions are satisfied. This is important because it allows us to say that p̂ is approximately normal.

TRACTOR SKIDDING HYPOTHESIS TESTING Forest engineers are interested in studying the skidding distances of tractors along a new road in a European Forest. The engineers collect data on a random sample of 12 tractors. The collected data (in meters) are: 350, 285, 574, 439, 295, 184, 261, 273, 400, 311, 141, 425. The average skidding distance for the sample of 12 tractors is 328.17 and the standard deviation is 118.46. Local loggers working on the road believe that the mean skidding distance of all tractors on this road is 325 meters. The engineers believe it is much greater than this. Conduct a hypothesis test based on the engineer’s belief. Conduct this hypothesis test at a significance level of .01. What conclusion can be made? Enter 1,2,3, or 4 in the box. Xbar is significantly greater than 325 feet. The average skidding distance of the tractors is significantly greater than 325 feet. µ is significantly greater than 325 feet. The average skidding distance of the tractors is significantly greater than 325 feet. Xbar is not significantly greater than 325 feet. The average skidding distance of the tractors is not significantly greater than 325 feet. µ is not significantly greater than 325 feet. The average skidding distance of the tractors is not significantly greater than 325 feet.

Consider an experiment in which a random family is selected among all families with exactly two children of which one is known to be a girl.

a. Write out the sample space and state the probability that the selected family has two girls.

b. Now consider an experiment in which we select a family randomly among all families with exactly two children, of which one is known to be a girl born on Tuesday. Write out the entire sample space taking into account the gender of the children and the day of the week they were born on.

c. What is the probability that the selected family has two girls?

d. Are the variables “day of the week” and “gender of child” dependent or independent?

A)While testing a building's fire alarms, the probability that any fire alarm will fail is 0.01. Suppose a building has 10 fire alarms, all which are independent of one another. The test will be passed if all fire alarms work.

a) 5 buildings are tested on the same day and each building has 10 fire alarms. How likely is it that 4 or more buildings pass the test? ( A building will pass if all 10 fire alarms are good)

B) Customers arrive at a restaurant according to a Poisson process at a rate of 30 customers per hour. There is a probability of 0.8 that a customer will dine in.

b) Say the customers are arriving independently of one another. What is the probability that 30 customers will arrive in a 1 hour time period AND all 30 will dine in?

C) Suppose a phd applicant is either accepted to a graduate program or not. if accepted the student can choose to attend or not attend. Suppose a graduate program has sent acceptance letters to 50 applicatns, but only had enough funding for 30 students. Let the students who were accepted to the program be independent of one another and the chance that a student will join the program be 0.6.

c) what is the probability that the graduate program will have enough funding for all students that joins the program.

Question 3 options:

The owner of the Britten's Egg Farm wants to estimate the mean number of eggs produced per chicken.  A representative random sample of 20 chickens show they produce an average of 25 eggs per month with a sample standard deviation (s) of 2 eggs per month. The distribution is known to be symmetrical and is close enough to normal to be treated as a normal distribution.

Answer the following questions related to the above paragraph and then calculate a 90% confidence interval for the mean number of eggs produced per chicken on the Britten's Egg Farm.

A What is the point estimate of the mean number of eggs produced per chicken?
       Enter answer with 0 decimal places (integer).

B Calculate the margin of error for the 90% confidence interval for the mean amount of eggs laid per month on the Britten's Egg Farm.

Enter answer rounded to 1 decimal point.
Include a zero to the left of the decimal point if the margin of error is a number between -1 and +1.

c The 90% conference interval for the mean number eggs produced per month is:

Enter the lower and upper limits for the conference interval by entering the lower limit first.
Rounded each conference limit to 1 decimal point.

D Prior to this study the owner of the Britten's Egg Farm Egg Farm believed the mean amount off eggs produced per month on his farm was 30.

Does the study support his belief with a 90% confidence?

a     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is not contained in the confidence interval.

b     Yes. The mean amount of eggs produced per month on his farm could be 30 per month because the number 30 is contained in the confidence interval.

c     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is not contained in the confidence interval.

d     No. The mean amount of eggs produced per month on his farm is most likely not 30 per month because the number 30 is contained in the confidence interval.

e    The owner can not comment on the mean amount of eggs produced per month on his farm because the confidence interval is based upon a sample.

Explain how you would process data for analysis of a qualitative research paper.

Dont worry about the amount of words, it's a short question.

A prisoner has to play a variation of the Monty Hall game with the jailer every day, not knowing which of the three doors the car is hidden behind. After the jailer's first choice, the prisoner therefore chooses one of the two remaining doors at random and opens it. In the event that he accidentally opens the door with the car, the jailer wins. If the jailer loses, the game must be played again the next day, with the car again hiding behind a random door. The prisoner may leave the cell as soon as the jailer has won the car.

Assume that the jailer plays with the "do not switch doors" strategy. What is the chance that the prisoner will be released after ten days? And how big is the chance that he will have to spend at least 10 days in jail?

In a study of speed​ dating, male subjects were asked to rate the attractiveness of their female​ dates, and a sample of the results is listed below ​(1 equals not ​attractive; 10 equals extremely ​attractive). Construct a confidence interval using a 99​% confidence level. What do the results tell about the mean attractiveness ratings of the population of all adult​ females? 6​, 8​, 1​, 10​, 6​, 4​, 7​, 7​, 9​, 9​, 5​, 8

How much time do you spend talking on your phone per day?

Guess the number of minutes you think you spend talking on the phone each day. This is your null hypothesis.

Secure the data from your phone for the past month and conduct a one sample hypothesis test of the mean length of your phone calls per day.   Be sure to show all your work by using excel and include your data set. Use a significance level of 0.05. You will have 30 data values showing the total of minutes you spend per day. (The easiest way to secure this data is to look at your "Recent" calls on your phone and list the total number of minutes that you have spent on the phone each day in the last 30 days. This will be the data that you will use.)

1) Please explain binomial approximation.
2) How can it be used in calculating population size?
3) Please provide an example.

Here comes BBA (Body-By-Agbegha) program again! A group of women of comparable age, weight and height was subjected to three weight loss treatments - BBA1, BBA2 and BBA3.   The table below shows the weight loss for the women.

Test to see whether there is any significant difference in the mean weight loss between the programs. Use a 5% level of significance.

State the null and alternative hypotheses.

Find the critical F value.

State a decision rule.

Find the value of the F Statistics.

Find the p-value.

State your decision.

Draw an appropriate conclusion using the context of the problem.

A random sample is drawn from a normally distributed population with mean μ = 18 and standard deviation σ = 2.3. [You may find it useful to reference the z table.]

Calculate the probabilities that the sample mean is less than 18.6 for both sample sizes. (Round intermediate calculations to at least 4 decimal places, “z” value to 2 decimal places, and final answer to 4 decimal places.)

The​ quality-control manager at a compact fluorescent light bulb​ (CFL) factory needs to determine whether the mean life of a large shipment of CFLs is equal to 7 comma 470 hours. The population standard deviation is 100 hours. A random sample of 64 light bulbs indicates a sample mean life of 7 comma 445 hours.

a. At the 0.05 level of​ significance, is there evidence that the mean life is different from 7 comma 470 hours question mark

b. Compute the​ p-value and interpret its meaning.

c. Construct a 95​% confidence interval estimate of the population mean life of the light bulbs.

d. Compare the results of​ (a) and​ (c). What conclusions do you​ reach?