University |
Republic Polytechnic (RP) |

Subject |
Specialist Diploma in Business Analytics |

**Question 1**

A sample of 26 offshore oil workers took part in a simulated escape exercise, resulting in the accompanying data on time (sec) to complete the escape.

389 356 359 363 375 488 325 394 402 373 373 370 364

366 364 325 339 393 392 369 374 359 356 443 334 397

- Are there any mild/extreme outliers in the sample? Explain your answer.
- Why is it important to identify the outliers for this set of data?

The simulated escape exercise was repeated after 6 months for the same 26 offshore oil workers. The below boxplot is produced the data for this repeated exercise

Do you think the repeated escape exercise is better or worse than the first exercise? Give an explanation for your answer.

b. Someone thinks that the escape time is symmetric.

389 356 359 363 375 488 325 394 402 373 373 370 364

366 364 325 339 393 392 369 374 359 356 443 334 397

Can you verify it? Give explanation for your answer.

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**Question 2**

The arrival of cars on a given highway is Poisson distributed. Let denotes the number of cars that arrive in one-hour duration during the rush hour. Thus,

Assuming answer the following questions:

a. What will happen if the highway is designed to carry only 20 cars during any hour? Explain your answer without computing any probability.

b. What will happen if the highway is designed to carry only 32 cars during any hour? Explain your answer without computing any probability.

c. Is it likely to have at least 23 cars arrive in a one-hour duration? Explain your answer.

**Question 3 **

In a particular IC fabrication process, a wafer contains 500 IC chips. The probability that a single chip is defective is 0.25. It can be assumed that the defects arise in a statistically independent manner. Let be the random variable defined as the number of non-defective chips on the wafer.

a. State a discrete distribution that can be used to model the distribution of

b. Is it likely that more than 354 chips on a wafer will pass the acceptance test? Explain your answer.

c. Approximate the distribution of as the normal distribution. Compute the probability in (b) using this approximation, and comment on the accuracy of the result

**Question 4 **A random variable X is used to model the time passengers for international flights are cleared. Assume that X is approximately normal and 95% of the passengers are cleared in 45 minutes.

a. If the standard deviation ( ) of X is 5 minutes, what is the meantime ( ) of X?

b. What would happen to if

- is more than 5 minutes
- is less than 5 minutes
- approaches 0

Explain your answer for all the 3 cases.

c. A passenger has 35 minutes from the time her flight lands to catch her transport. Assuming a standard deviation of 10 minutes, what is the likelihood that she will be cleared in time? Explain your answer.

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**Question 5 **

The weights of canned food products in ABC Company follow the normal distribution, with a mean of 9.20 pounds and a standard deviation of 0.25 pounds. The label weight is given as 9.00pound.

a. What proportion of the food product actually weighs less than the amount claimed on the label?

b. Two proposals are suggested to reduce the proportion of the food product below label weight.

- Proposal 1: Increase the mean weight to 9.25 and leave the standard deviation the same.
- Proposal 2: Leave the mean weight at 9.20 and reduce the standard deviation from 0.25 pounds to 0.15.

Which proposal would you recommend?

**Question 6**

In a study of certain flu viruses, the random variable X is used to model the number of infected patients from different parts of Singapore. Past experience indicates that the standard deviation of X is 5. If the mean of X exceeds 10, then the flu virus infection will be classified as an epidemic.

The following is a recently collected sample of the number of infected patients:

7 8 4 5 9 9 4 12 8 1 8 7

3 13 2 1 17 7 12 5 6 2 1 13

14 10 2 4 9 11 3 5 12 6 10 7

a. What is the approximate distribution of the sample mean? Explain your answer.

b. Find a 95% confidence interval on the mean of X. Can we infer that there is no epidemic? Explain your answer.

c. Can we make the same inference as in (b) under a 98% confidence interval? Explain your answer.

**Question 7 **

The calibration of a scale is to be checked by weighing a 10-kg test specimen 25 times. Suppose that the results of different weighing are independent of one another and that the weight on each trial is normally distributed with =0.2kg. Let denote the true average weight reading on the scale.

a. What hypotheses should be tested?

b. Suppose the scale is to be recalibrated if the sample data shows a mean of greater than 10.1032 or shows a mean of less than 9.8968, what is the probability that recalibration is carried out when it is actually unnecessary?

c. If the recalibration is judged unnecessary when in fact =10.1, what type of error is committed?

d. If the sample size were only 10 rather than 25, list the steps taken to test the hypotheses under =0.05.

e. Using the steps listed in part (d), what would you conclude from the following sample data:

9.981, 10.006, 9.857, 10.107, 9.888, 9.728, 10.439, 10.214, 10.190, 9.793

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