Use This Sheet To Answer Question 1. Put A Box Around Your A

Use this sheet to answer question 1. Put a box around your answer

Part 1use This Sheet To Answer Question 1 Put A Box Around Your Answe

Part 1use This Sheet To Answer Question 1 Put A Box Around Your Answe

Part 1 Use this sheet to answer question 1. Put a box around your answer. Round your answer to 4 decimal places. Part 2 Use this sheet to answer question 2. Put a box around your answers.

For parts a and b, round your answers to 4 decimal places. Part 3 Use this sheet to answer question 3. Put a box around your answer. Round your answer to 1 decimal places. Part 4 Use this sheet to answer question 4.

Put a box around your answers. Round your answers to 4 decimal places. Flaws Flaws, x Probability, P(x) 0 0.....038 Part 6 Color Model Blue Brown White XB​- FL​- Use this sheet to answer question 6. Put a box around your answers. Round your answers to 4 decimal places.

Bus224 Exam-2 Total Points: 100 Read carefully before starting your exam Before you start working on any part of this exam, save the Exam_2 file as Exam_2_your full name . To submit your file, log on to this course’s blackboard site, click on Exams/ Take-home Exam tab. Then, click on Exam-2 and upload your file. Keep in mind – you can submit your file only once. [Note: In order to receive full credits, you must show your work i.e. your Excel work.] 1. The file name Exam-2 , sheet named Part 1 is kept blank.

Use Part 1 sheet to answer this question. Put a box around your answer. Round your answers to 4 decimal places. Ship collisions in the Houston Ship Channel are rare. Suppose the number of collisions are Poisson distributed, with a mean of 1.2 collisions every four months.

What is the probability of having less than two collisions over a four-month period? [10 points] 2. The file name Exam-2 , sheet named Part 2 is kept blank. Use Part 2 sheet to answer this question. Put a box around your answers. For (a) and (b), round your answers to 4 decimal places.

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. a) What is the probability that more than seven of them say job stress caused frequent health problems? b) What is the probability that exactly five say job stress caused frequent health problems? c) What is the expected [mean] number of workers that would say job stress caused frequent health problems? [Hint: Use binomial distribution to answer question 2] [10 + 5 + 5 = 20 points] 3. The file name Exam-2 , sheet named Part 3 is kept blank. Use Part 3 sheet to answer this question.

Put a box around your answer. Round your answer to 1 decimal places. The U.S. national average door-to-doctor wait time for patients to see a doctor is now 21.3 minutes. Suppose such wait times are normally distributed with a standard deviation of 6.7 minutes. Some patients will have to wait much longer than the mean to see the doctor.

In fact, based on this information, 3% of patients still have to wait more than how many minutes to see a doctor? [15 points] 4. The file name Exam-2 , sheet named Part 4 is kept blank. Use Part 4 sheet to answer this question. Put a box around your answers. Round your answers to 4 decimal places.

According to CBS Money Watch, the average monthly household cellular phone bill is $100. Suppose monthly household cell phone bills are normally distributed with a standard deviation of $11.35. a) What is the probability that a randomly selected monthly cell phone bill is more than $127? b) What is the probability that a randomly selected monthly cell phone bill is between $87 and $110? c) What is the probability that a randomly selected monthly cell phone bill is no more than $82? [7.5 + 10+ 5 = 22.5 points] 5. The file Exam-2, sheet named Flaws, lists the discrete distribution of the number of flaws found in a porcelain cup produced by a manufacturing firm. Use these data and the associated probabilities to compute the expected number of flaws and the standard deviation of flaws. [Note: Use Excel to calculate the expected value and the standard deviation of flaws.

Show your work on Flaws sheet. Do not create a new sheet or a new workbook.] [5 + 7.5 = 12.5 points] 6. Use Part 6 sheet to answer this question. Put a box around your answers. A bicycle company makes two mountain bike models that each come in three colors. The following table shows the production volumes for last week: Color Model Blue Brown White XB​- FL​- a) Based on the relative frequency assessment​ method, what is the probability that a manufactured item is white​? [Round your answer to 4 decimal places] b) What is the probability that a product manufactured is an XB-50 and white? [Round your answer to 4 decimal places] c) Given that a product manufactured is FL-99, what is the probability that item is white? [Round your answer to 4 decimal places] [2.5 + 5 + 12.5 = 20 points]

Paper For Above instruction

The Houston Ship Channel experiences rare ship collisions, which follow a Poisson distribution with an average of 1.2 collisions over four months. To determine the probability of having fewer than two collisions within this period, we utilize the Poisson probability formula. This calculation is essential for understanding risk management and safety protocols in maritime environments. The Poisson probability of observing exactly x events is given by P(x) = (λ^x e^(-λ)) / x!, where λ is the expected number of events.

Given λ = 1.2, the probability of fewer than two collisions (i.e., zero or one collision) is P(X

P(0) = (1.2^0 e^(-1.2)) / 0! = e^(-1.2) ≈ 0.3012

P(1) = (1.2^1 e^(-1.2)) / 1! = 1.2 * e^(-1.2) ≈ 0.3614

Adding these: 0.3012 + 0.3614 = 0.6626

Therefore, the probability of fewer than two collisions in four months is approximately 0.6626.

Moving to question 2, a binomial distribution models the probability that a certain number of workers (out of 10) perceive job stress as a cause of health problems. With a probability of success p = 0.7 for each worker, we compute:

  • a) The likelihood that more than seven workers (i.e., 8, 9, or 10) report stress-related health issues. This involves calculating P(X > 7) = P(8) + P(9) + P(10). Using binomial probability formula P(k) = C(n, k) p^k (1-p)^{n-k}.
  • b) The probability exactly five workers (k=5) cite job stress as a cause, calculated as P(5).
  • c) The expected number (mean) of workers reporting stress is μ = np = 10 * 0.7 = 7.

Question 3 involves the normal distribution, assessing the wait time for patients. With a mean of 21.3 minutes and standard deviation 6.7, the wait time that exceeds 97% of patients corresponds to the 97th percentile of the distribution. Using the z-score formula, Z = (X - μ) / σ, where Z is the z-value for 97%, from standard normal tables Z ≈ 1.88.

Calculating X = μ + Z σ = 21.3 + 1.88 6.7 ≈ 21.3 + 12.6 = 33.9 minutes.

Thus, about 3% of patients wait more than approximately 33.9 minutes.

In question 4, the distribution of household cell phone bills is normal with mean $100 and standard deviation $11.35. The probability that a bill exceeds $127 is found by calculating the Z-score:

Z = (127 - 100) / 11.35 ≈ 2.42. Looking up Z = 2.42, the probability of exceeding this Z-value is about 0.0078.

Similarly, for bills between $87 and $110, Z-scores are:

Z₁ = (87 - 100) / 11.35 ≈ -1.14

Z₂ = (110 - 100) / 11.35 ≈ 0.88

The probabilities are P(Z

For bills no more than $82, Z = (82 - 100) / 11.35 ≈ -1.58, and P(Z

The analysis of flaws in porcelain cups involves calculating the expected value and standard deviation from the data, which can be done using Excel's functions such as SUMPRODUCT for the expected value and formulas for variance and standard deviation.

The last question addresses probability assessments using a relative frequency method based on production data for mountain bikes. Calculations involve dividing the volume of white-colored, XB-50 models by total production volume to get the probability of selecting a white item, then similarly for joint probabilities and conditional probabilities for specific model and color combinations.

References

  • Casella, G., & Berger, R. L. (2002). Statistical Inference. Duxbury Press.
  • Mendenhall, W., Ott, L., & Buchanon, J. (2013). Elementary Statistics: A Step-by-Step Approach. Cengage Learning.
  • Devore, J. L. (2011). Probability and Statistics for Engineering and the Sciences. Cengage Learning.
  • Ross, S. M. (2014). Introduction to Probability Models. Academic Press.
  • Moore, D. S., & McCabe, G. P. (2006). Introduction to the Practice of Statistics. W. H. Freeman.
  • Newbold, P., Carlson, W. L., & Thorne, B. (2013). Statistics for Business and Economics. Pearson.
  • Wasserman, L. (2004). All of Statistics. Springer.
  • Gelman, A., et al. (2013). Bayesian Data Analysis. CRC Press.
  • Hogg, R. V., McKean, J., & Craig, A. T. (2013). Introduction to Mathematical Statistics. Pearson.
  • Stuart, A., & Ord, J. K. (2010). Kendall's Advanced Theory of Statistics. Wiley.

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