Question

1. An engineering student wants to select a carbon steel workpiece for a prototype of a robot arm. There are multiple material properties that should be considered, therefore the student decided to assume that the all the Carbon Steels listed in the table as homogeneous for Brinell Hardness. Which of the following statement(s) is (are) true about outliers of Brinell Hardness?

1. 1. 1095 normalized at 1650 F is a low outlier
2. 2. 1030 quench & temper at 400 F is a high outlier
3. 3. 1050 quench & temper at 400 F is a high outlier

1. Only (i) is correct
2. Only (i) and (iii) are correct
3. Only (ii) and (iii) are correct

2. A student in STAT 325 class was too lazy, therefore she didn’t study anything for the final exam. She decided to just randomly pick answers for all the multiple-choice questions (MCQs). Note that there are 12 MCQs, and the probability that a randomly chosen answer being correct is 1/3. What are the mean and variance of the possible number of correctly answered questions in her final exam?                                                                                   

1. Mean is 4, Variance is 2.7
2. Mean is 3, Variance is 4
3. Mean is 2, Variance is 1.6

3. Overall odds of winning a prize in mega-millions is approximately 1/15, and the numbers in each ticket is independent of the others. Richard bought two mega-million tickets, his probability of winning the first OR the second ticket is:                                                                                                                                                                         

1. 0.0667
2. 0.1333
3. 0.1289

4. The data indicate that 10.5% of people with a Cardiovascular Disease who were diagnosed with COVID-19 died. The data also indicate that this percentage for Diabetes is 7.3%, for Chronic Respiratory Disease is 6.3%, Hypertension is 6%, Cancer is 5.6% and No health conditions is 0.9%. Of patients in a certain COVID-19 treatment center, 35% have cardiovascular diseases, 15% have diabetes, 20% have chronic respiratory diseases, 15% have hypertension, 4% have cancer and the other 11% have no health conditions. The total mortality rate at this treatment center should be:                                                                                                                                                

1. 36.6%
2. 9.3%
3. 16.7%

Answer 1

1. The option c is the right answer, because for 1030 quench and 1050 quench the temper at 400 F is low and seems outliers of the Brinell Hardness. 2. Total MCQs, n=12 Probability that randomly chosen answer is correct, p= 3 The probability is same for the question. So, the binomial distribution is applicable. The mean of the binomial distribution=np 1 Hence, the mean=12x= 3 = 4 The variance of binomial distribution = np(1-p) 1 =12x=x 1 Hence, the variance = 2.67

Hence, the option a is the right answer. 3. 1 The probability of winning a prize in mega-millions = 15 The numbers in each ticket is independent of each other. 1 P (of winning the first ticket) 15 1 14 P (of winning the second ticket) 15 15 14 225 Hence, P (of winning the first or second ticket) 1 14 + 15 225 29 225 = 0.1289 Hence, the option c is the right answer.

4. Total deaths = 10.5%+7.3% +6.3% +6%+5.6%+0.9% = 36.6% Total population=35%+15%+ 20% +15%+4%+11% = 100% Total mortality rate= total death total population 36.6% 100% = 36.6% Hence, the option a is the right answer.