On September​ 11, 2002, a particular state​ lottery's daily number came up 9 - 1 - 1. Assume that no more than one digit is used to represent the first nine months.

​a) What is the probability that the winning three numbers match the date on any given​ day?​

b) What is the probability that a whole year passes without this​ happening? ​

c) What is the probability that the date and winning lottery number match at least once during any​ year? ​

d) If 27 states have a​ three-digit lottery, what is the probability that at least one of them will come up 3 - 1 - 0 on March 10​?

MERMED Inc. is a medical device manufacturer.

The company’s headquarters is located in Houston, Texas. It is a global leader in developing, manufacturing, selling and servicing diagnostic imaging and therapeutic medical devices used to diagnose and treat cardiovascular and other diseases. MERMED earned $300 million of revenue in 2015, while employing more than 10,000 people worldwide. One of it’s manufacturing plants is located in Dingle, Co. Kerry, Ireland. Tom Jones is the plant manager at the Dingle facility.

The Dingle site runs 12 hour shifts, 7 days a week. It has 1000 employees. It manufactures a variety of of medical devices (including Class III devices). A number of it's products are sold in the US and European markets. The facility has a Quality Management System in place. Their Quality Management System is in compliance with ISO 13485:2016 and 21 CFR 820. Their facility is frequently audited by Notified Bodies and the FDA.

The site was recently audited by corporate. The corporate auditing team were checking the site's compliance with ISO 13485:2016 and 21 CFR 820. The auditors found a number of potential non-conformances to  ISO 13485:2016 and 21 CFR 820.

You must complete 4 tasks (for each of the 5 incidents/questions):

1. Review each of these potential non-conformances (5 incidents in total)

2. Determine if they are non-conformances against the requirements of the ISO13485:2016 AND 21 CFR 820.

3. If they are non-compliances, write down the specific clause numbers in ISO 13485:2016 AND specific section number of 21 CFR 820 which is applicable (write down the main clause/section in each regulation that the non-compliance is against).

4. Briefly EXPLAIN your decision.

The company has not established a sampling plan for the evaluation of products during incoming inspection of Component ID Z2906.

True or False

1) If the alternative hypothesis of an ANOVA F-test is true, we expect MSG to be less than MSE. test

2) An F distribution depends on two differrent degrees of freedom, one for numerator and the other for denominator.

3) If the conditional distributions in a two-way table are similar to each other, one can conclude that the two variables in the two-way table are associated.

4) In a two-way table, if the expected counts are about the same as the observed counts, the P-value of the chi-square statistic is close to zero.

6) Consider an ANOVA procedure to compare four population means. Thus, the total number of pairs to be considered in multiple comparisons is six. If the probability that the null hypothesis is falsely rejected in each pair is equal to 0.01, the probability that the null hypothesis is falsely rejected at least once in all six pairs is approximately (Use an approximation formula and give your answer to two decimal places.)

1. Complete the pension worksheet using the information provided below:

2020 records of Lexxus Company provided the following data related to its noncontributory defined benefit pension plan.

ACCOUNT BALANCES (‘000s)    Jan. 1, 2020                Activity (‘000s)                                              2020

Projected Benefit Obligation $300 cr                                    Service cost                                                     $ 50

Plan Assets                             170 dr                                    Contributions                                                  110

Accumulated OCI – PSC            40 dr                                    Actual return on plan assets                                 8

Accumulated OCI - G/L            25 dr                                    Amortization of PSC                                          4

Remaining Service Life              10 years                               Pension benefits paid to retirees                       124

OTHER                                                         

Expected rate of return on plan assets            6%

Discount/Settlement rate                                8%

2. Perform the corridor test of OCI-Gains/Losses. Show your work here:
3. Provide the end of year journal entry based on worksheet amounts.
4. Explain the difference between a defined contribution pension plan and a defined benefit pension plan. Explain how the employer’s obligation differs between the two types of plans.

1. When proving If p then q.”

DIRECT PROOF you need to:

CONTRAPOSITION you need to:

CONTRADICTION you need to:

2. Prove by direct proof that if m and n are integers, with m odd and n is even, then 5n + m2 is odd.

3. Prove by contraposition that if x 6= 5 and is irrational, then 4x x − 5 is irrational.

4. Prove the following existential statements by providing a value for x. In both cases, the universe is the set of all real numbers.

a) ∃x x 2 + 5x − 7 = 0

b) ∃x x < 10 → (x − 2) 2 < 0

5. Prove that for any integer n, there exists an even integer k so that n < k + 1 < n + 3.

6. Prove or disprove: If x is rational and y is irrational, then xy is irrational.

7. Prove that there is no positive integer n so that 49 < n 2 < 64.

8. Prove or disprove: ∀x∃y ((x − 3)y = 4x), where the universe of discourse is R for both variables.

9. Prove, by contraposition, that if the product of two real numbers is irrational, then at least one of the two numbers is irrational. (In other words: If x · y is irrational, then x is irrational OR y is irrational.”)

10. Prove, by contradiction, that √ 3 is irrational. You may use the Little Theorem: If m2 is a multiple of 3, then m itself is a multiple of 3

A personal fitness company produces both a deluxe and a standard model of a smoothie blender for home use. Selling prices obtained from a sample of retail outlets follow.

(a)

The manufacturer's suggested retail prices for the two models show a $10 price differential. Use a 0.05 level of significance and test that the mean difference between the prices of the two models is $10.

Calculate the value of the test statistic. (Round your answer to three decimal places.)

Calculate the p-value. (Round your answer to four decimal places.)

(b)

What is the 95% confidence interval for the difference between the mean prices of the two models (in dollars)? (Round your answers to nearest cent. Use the mean price for the deluxe model − the mean price for the standard model.)

$ to $

p-value =

Consider an MNC has two choices on investment. One of them is to invest the project in Taiwan only. The other is to invest 75% funds in Taiwan and 25% in Singapore. Both investments give the same return. The standard deviation of exchange movements is 7% for Taiwan dollars and 5% for Singapore dollars. The correlation coefficient between movements in the value of the Taiwan dollar and the Singapore dollar is .7. Based on this information, which investment should the MNC chose? Show the calculations

A bag of 30 tulip bulbs contains 13 red tulip​ bulbs, 10 yellow tulip​ bulbs, and 7 purple tulip bulbs. Suppose two tulip bulbs are randomly selected without replacement from the bag.

(a) What is the probability that the two randomly selected tulip bulbs are both​ red?

​(b) What is the probability that the first bulb selected is red and the second​ yellow?

​(c) What is the probability that the first bulb selected is yellow and the second​ red?

​(d) What is the probability that one bulb is red and the other​ yellow?

A 3.0 kg cart moving to the right with a speed of 1.0 m/s has a head-on collision with a 5.0 kg cart that is initially moving to the left with a speed of 2.0 m/s. After the collision, the 3.0 kg cart is moving to the left with a speed of 1.0 m/s.

a. What is the final velocity of the 5 kg cart?

b. Determine the speed of the center of mass of the two carts before and after the collision.

c. If instead, the two carts stuck together after the collision, what would be their common velocity?

d. Determine the amount of kinetic energy lost in the collisions described in (a) and (c). State the type of collision in parts (a) and (c) and suggest a reason for the loss of total energy after the collision.

QUESTION 2 [20] The number of aces served by Novak Djokovic in the last 20 tournaments that he has participated in, is shown below. 12 17 13 7 8 14 11 14 10 12 15 9 11 13 6 15 18 5 19 24 2.1. Using the raw data, determine the range. (2) 2.2. Group the data into a frequency distribution with a lowest class lower limit of 1 ace and a class width of 5 aces. (7) 2.3. Determine the mean number of aces served, using the raw data. (3) 2.4. Draw a less than OGIVE curve corresponding to the data and use it to estimate the median. (8).