Your leader wants you to evaluate the difference in cycle time between three different offices. Describe the steps you would take in the evaluation in order to provide a report so the leader can take action.

In a recent study on world​ happiness, participants were asked to evaluate their current lives on a scale from 0 to​ 10, where 0 represents the worst possible life and 10 represents the best possible life. The mean response was 5.8 with a standard deviation of 2.3.

​(a) What response represents the 91st ​percentile? ​

(b) What response represents the 65th ​percentile?

​(c) What response represents the first ​quartile?

How can one of the attributes control charts (p, np, c or u) could be used to stabilize the process? Can you please give an example of a process from a quality perspective?

Suppose that, on average, electricians earn approximately μ = 54, 000 dollars per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = 12, 000.

1. (3 points) What is the probability that a randomly selected electrician's salary is more than $50,000 but less than $60,000?

2. (3 points) Tax code dictates that 40% income tax is applied to the electricians whose annual income is among top 5% in the population. What is the minimum yearly earnings that will be levied by 40% tax, i.e., ?nd the constant a such that Pr{X > a} = 5%.

3. (3 points) In a sample of four electricians, what is the probability that all four electricians' salaries are more than $50,000 but less than $60,000? (Please round your answer to 4 decimal places.)

4. (3 points) In a sample of four electricians, let X ̄ be the average yearly earnings of these four electricians. What is the expectation of the average earnings, i.e., E(X ̄) =?

5. (3 points) In a sample of four electricians, let X ̄ be the average yearly earnings of these four 9electricians. What is the standard deviation of the average earnings, i.e., s.e.(X ̄ ) =?

6. (3 points) Is the average earnings among four electricians, X ̄, normally distributed or not? Please explain. (No credit if there is no explanation.)

7. (3 points) What is the probability that the average salary of four randomly selected electricians is more than $50,000 but less than $60,000, i,e, Pr{50, 000 < X ̄ < 60, 000}? (If you are able to ?nd this probability, please show your answer; if you are not able to ?nd this probability, please explain why you can not.)

8. (4 points) What is the probability that the average salary of sixteen randomly selected electricians is more than $50,000 but less than $60,000 ? (If you are able to ?nd this probability, please show your answer; if you are not able to ?nd this probability, please explain why you can not.)

In the country of United States of Heightlandia, the height measurements of ten-year-old children are approximately normally distributed with a mean of 55.6 inches, and standard deviation of 3.4 inches.

A) What is the probability that a randomly chosen child has a height of less than 57.7 inches?

Answer= (Round your answer to 3 decimal places.)

B) What is the probability that a randomly chosen child has a height of more than 47.2 inches?

Answer= (Round your answer to 3 decimal places.)

The systolic blood pressure of adults in the USA is nearly normally distributed with a mean of 117 and standard deviation of 21 .

Someone qualifies as having Stage 2 high blood pressure if their systolic blood pressure is 160 or higher.

a. Around what percentage of adults in the USA have stage 2 high blood pressure? Give your answer rounded to two decimal places.

%





b. If you sampled 2000 people, how many would you expect to have BP> 160? Give your answer to the nearest person. Note: I had a bit of an issue encoding rounded answers, so try rounding both up and down if there's an issue!

people





c. Stage 1 high BP is specified as systolic BP between 140 and 160. What percentage of adults in the US qualify for stage 1?

%



d. Your doctor tells you you are in the 30th percentile for blood pressure among US adults. What is your systolic BP? Round to 2 decimal places.

lbs

Consider the following data on distances traveled by 100 people to visit the local park.

Expand and construct the table adding columns for relative frequency and cumulative relative frequency. Then plot Histogram, Frequency Polygon and Ogive Curve.

A box in a certain supply room contains four 40-W lightbulbs, five 60-W bulbs, and seven 75-W bulbs. Suppose that three bulbs are randomly selected. (Round your answers to four decimal places.)

(a) What is the probability that exactly two of the selected bulbs are rated 75-W?

(b) What is the probability that all three of the selected bulbs have the same rating?

(c) What is the probability that one bulb of each type is selected?

(d) Suppose now that bulbs are to be selected one by one until a 75-W bulb is found. What is the probability that it is necessary to examine at least six bulbs?

Question 6

In a recent sample of 84 used car sales costs, the sample mean was $6,425 with a sample standard deviation of $3,156.

Assume the underlying distribution is approximately normal.

Part I) Which distribution should you use for for determining a confidence interval for estimating the population mean for used car sales costs?

a   Normal Distribution

b     t Distribution

c     Uniform

d     Chi Sq distribution

Part II) What is the number of degrees of freedom (df) for this problem.

Par III) Define the random variable X by selecting the appropriate letter below.

a     An individual data item randomly selected from the population, some times referred to as the parent population.

b     The average of n individual data item randomly selected from the parent population. In this question n is 84.

Part IV) Define the random variable X ¯ (Xbar) by selecting the appropriate letter below.

c     An individual data item randomly selected from the population, sometimes referred to as the parent population.

d     The average of n individual data item randomly selected from the parent population. In this question n is 84.

Part V) Construct a 95% confidence interval for the population mean time wasted.

Enter your answers rounded to 0 decimal places (Enter answer as an integer).

In the two answer locations provided enter the lower bound of the confidence interval first followed by the upper bound.

Part VI)

What is meant by the term “95% confident” when constructing a confidence interval for a mean?

a.    If we took repeated samples, approximately 95% of the samples would produce the same confidence interval.

b     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the sample mean.

c     If we took repeated samples, the sample mean would equal the population mean in approximately 95% of the samples

d     If we took repeated samples, approximately 95% of the confidence intervals calculated from those samples would contain the true value of the population mean.

Calculate the value for the marked cell (?).

Question 7 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 25 chickens show they produce an average of 20 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 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     What is the appropriate distribution for calculating a 90% confidence interval?

c The degrees of freedom (df) for this problem is?
Enter Na or 0 for the df if the appropriate distribution does not required a df.

e     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.

F     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 22.

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 22 per month because the number 22 is not contained in the confidence interval.

b     Yes. The mean amount of eggs produced per month on his farm could be 22 per month because the number 22 is contained in the confidence interval.

c     No. The mean amount of eggs produced per month on his farm is most likely not 22 per month because the number 22 is not contained in the confidence interval.

d     No. The mean amount of eggs produced per month on his farm is most likely not 22 per month because the number 22 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.

Enter the correct answer by selecting and entering the appropriate letter.

Decisions about alpha level may be different, especially as it relates from hard sciences to social sciences. For example, a medical trial for cancer treatments conducts their statistical tests at .0001 – so for every 1 out of 10,000 patients, there may be issues, sickness or even death. For social science, we use alpha .05. We are comfortable with performing research, for example, on students. So we are satisfied with losing 5 out of 100 students or having our results being incorrect 5 out of 100 times. Do you agree with these alpha levels? Why or why not? What if your child’s education and the teacher assigned to him/her would be successful 95 out of 100 times?

The distribution of online sale price for four-year-old Harley-Davidson touring motorcycles is approximately Normally distributed with a mean of $15,000 and a standard deviation of $4,000.

(A) Mr. Rampal plans to spend between $9,000 and $12,000 on one of these motorcycles. What proportion of the available motorcycles of this type can he afford?

(B)What is the 30th percentile for the prices of motorcycles of this type?

(C)Show that a motorcycle of this type priced at $28,000 is considered an outlier by the 1.5xIQR rule.

This is an introduction to social science research methods course:

Imagine you’re planning to estimate the price of the average book at your college bookstore.

The bookstore carries 13,000 titles, but you plan to sample only 200 books.

You will select a sample of 200 books, record the price of each book, and use the average of the 200 books to estimate the average price of the 13,000 titles in the bookstore.

Assume that the bookstore can give you access to a database that lists all 13,000 titles that it carries.

Based on this information, clearly answer the following questions?

How might you collect a cluster sample?

How might you collect a quota sample?