Master Engineering Applications with Applied Mathematics

Question 1

In engineering, which probability distribution is most suitable for representing the time between failures of an electronic component?

Accepted Answer

Exponential distribution

Answer

Binomial distribution

Answer

Poisson distribution

Answer

Normal distribution

Question 2

Which statistical technique is primarily used to analyze the variability present within an engineering dataset?

Accepted Answer

Analysis of variance

Answer

Regression analysis

Answer

Sampling

Answer

Correlation analysis

Question 3

In the context of quality control, what does the term 'acceptance sampling' refer to?

Accepted Answer

Assessing a sample of products to determine if the entire lot meets specified quality standards

Answer

Testing each individual product in a lot to ensure its quality

Answer

Employing statistical methods to predict the quality levels of future products

Answer

Identifying the root causes of product defects

Question 4

Which probability distribution is commonly utilized to model the intervals between failures of engineering components?

Accepted Answer

Exponential distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Poisson distribution

Question 5

Which statistical test is employed to determine if two sets of engineering data possess significantly different means?

Accepted Answer

T-test

Answer

Chi-squared test

Answer

F-test

Answer

ANOVA

Question 6

What is the primary role of statistical sampling in the field of engineering?

Accepted Answer

Obtaining information about a population from a smaller sample

Answer

Ensuring that all products in a lot are tested

Answer

Determining the exact probability of product defects

Answer

Evaluating the performance of manufacturing processes

Question 7

What is the significance of the failure rate in reliability analysis?

Accepted Answer

It represents the likelihood of a failure occurring over a specified time interval

Answer

It indicates the average time between failures

Answer

It determines the mean time to repair

Answer

It specifies the life expectancy of a system

Question 8

Which probability distribution is commonly utilized to model the number of defects present in a manufactured item?

Accepted Answer

Poisson distribution

Answer

Normal distribution

Answer

Binomial distribution

Answer

Exponential distribution

Question 9

Describe the distinction between a Type I and a Type II error in the context of statistical hypothesis testing.

Accepted Answer

Type I error occurs when the null hypothesis is incorrectly rejected, while Type II error occurs when the null hypothesis is incorrectly accepted

Answer

Type I error occurs when the null hypothesis is correctly accepted, while Type II error occurs when the null hypothesis is incorrectly rejected

Answer

Type I error is more severe than Type II error

Answer

Type II error is more severe than Type I error

Question 10

How does integrating statistical quality control techniques into the design process of engineering products contribute to enhancing product quality?

Accepted Answer

Identifies and mitigates potential defects during design, leading to improved reliability and performance

Answer

Reduces testing time and resources by optimizing the design for quality

Answer

Optimizes material usage and production processes, lowering manufacturing costs

Answer

Eliminates the need for post-production testing, ensuring products meet quality standards before reaching customers

Question 11

Which of the following is NOT a crucial aspect of quality control in engineering?

Accepted Answer

Redesigning the product

Answer

Prevention of defects

Answer

Monitoring of processes

Answer

Seeking customer feedback

Question 12

In reliability analysis, which statistical distribution is often used to model the time between failures?

Accepted Answer

Exponential distribution

Answer

Normal distribution

Answer

Poisson distribution

Answer

Binomial distribution

Question 13

Which sampling method allows for the inspection of a large population without testing every item?

Accepted Answer

Acceptance sampling

Answer

Random sampling

Answer

Systematic sampling

Answer

Stratified sampling

Question 14

A process capability index (Cpk) of 1.67 indicates that the process is:

Accepted Answer

Highly capable

Answer

Moderately capable

Answer

Not capable

Answer

Very capable

Question 15

Which hazard analysis technique involves the identification and categorization of potential hazards?

Accepted Answer

Failure Mode and Effects Analysis (FMEA)

Answer

Fault Tree Analysis (FTA)

Answer

Event Tree Analysis (ETA)

Answer

Markov Analysis

Question 16

Within the context of engineering, 'reliability growth' refers to:

Accepted Answer

The increase in system reliability over time due to the correction of design flaws

Answer

The decrease in system reliability over time due to wear and tear

Answer

The system's ability to recover from a failure

Answer

The likelihood of a system failing within a specified time period

Question 17

Which of the following is NOT a type of probability distribution commonly used in engineering reliability analysis?

Accepted Answer

Binomial distribution

Answer

Normal distribution

Answer

Exponential distribution

Answer

Weibull distribution

Question 18

What is the primary purpose of a control chart in quality control?

Accepted Answer

To monitor a process and identify out-of-control conditions

Answer

To predict future process performance

Answer

To determine the optimal process parameters

Answer

To evaluate the effectiveness of a new process improvement

Question 19

What is the fundamental difference between reliability and availability?

Accepted Answer

Reliability measures the ability of a system to function as expected, while availability measures the ability to restore a system to operation.

Answer

Reliability measures the probability of failure, while availability measures the time to repair.

Answer

Reliability and availability are synonymous.

Answer

Availability measures the ability to function as expected, while reliability measures the time to repair.

Question 20

In hypothesis testing, what does the p-value represent?

Accepted Answer

The probability of obtaining the observed results if the null hypothesis is true

Answer

The level of confidence in rejecting the null hypothesis

Answer

A measure of the effect size

Answer

The probability of making a Type I error

Question 21

Which of the following is an advantage of using simulation in engineering reliability analysis?

Accepted Answer

It can handle complex systems and scenarios

Answer

It provides accurate results in all cases

Answer

It is less time-consuming than analytical methods

Answer

It eliminates the need for physical testing

Question 22

What is the key distinction between a discrete and a continuous probability distribution?

Accepted Answer

Discrete distributions take only integer values, while continuous distributions take any value within a range

Answer

Continuous distributions take only integer values, while discrete distributions take any value within a range

Answer

Discrete distributions are used for counting events, while continuous distributions are used for measuring variables

Answer

Continuous distributions are used for counting events, while discrete distributions are used for measuring variables

Question 23

In engineering, the 'infant mortality' phase of the bathtub curve refers to a period of high failure rate early in a product's life. Explain this phase and its implications for product design and lifecycle management.

Accepted Answer

The infant mortality phase is characterized by a high failure rate due to manufacturing or design defects, helping identify areas for improvement and optimize production processes.

Answer

The infant mortality phase represents a period of low failure rate as the product matures and stabilizes, indicating a well-designed and reliable product.

Answer

The infant mortality phase is a period of increasing failure rate as the product ages and degrades, signifying the end of its useful life.

Question 24

In a survey of 500 customers, 250 indicate satisfaction with a particular product. Construct a 99% confidence interval for the proportion of satisfied customers in the population.

Accepted Answer

(0.47, 0.53)

Answer

(0.37, 0.63)

Answer

(0.42, 0.58)

Answer

(0.52, 0.68)

Question 25

A company wants to estimate the average monthly sales of a particular product. They collect data from a random sample of 12 months and calculate a mean of $\$10,000$ with a sample standard deviation of $\$2,000$. Assuming a normal distribution, the 90% confidence interval for the average monthly sales is:

Accepted Answer

(\$9,280, \$10,720)

Answer

(\$9,500, \$10,500)

Answer

(\$9,400, \$10,600)

Answer

(\$9,080, \$10,920)

Question 26

Which chart type is NOT typically used for quality control in engineering?

Accepted Answer

Pie chart

Answer

Control chart

Answer

Histogram

Answer

Pareto chart

Question 27

Which of these measures describes the spread or dispersion of data points in a dataset?

Accepted Answer

Standard deviation

Answer

Mean

Answer

Median

Answer

Mode

Question 28

A bag holds 5 red balls and 7 blue balls. What is the probability of randomly picking a red ball?

Accepted Answer

5/12

Answer

5/7

Answer

1/2

Answer

7/12

Question 29

Which of the following is a common source of error when selecting samples for analysis in engineering?

Accepted Answer

Bias in the sample selection process

Answer

Limited accuracy of the measuring instruments used

Answer

Random fluctuations inherent in data collection

Answer

The overall size of the sample collected

Question 30

In a hypothesis test, what does the null hypothesis typically state?

Accepted Answer

There's no significant difference or relationship between the variables being studied.

Answer

The sample size is large enough to draw valid conclusions.

Answer

The data follows a normal distribution pattern.

Answer

There's a significant difference or relationship between the variables being studied.

Question 31

What type of engineering test involves applying a load to a specimen until it breaks to evaluate its strength?

Accepted Answer

Destructive testing

Answer

Diagnostic testing

Answer

Non-destructive testing

Answer

Proof testing

Question 32

A manufacturer produces steel beams with a target mean strength of 500 MPa. A random sample of 25 beams has a sample mean strength of 495 MPa and a sample standard deviation of 10 MPa. Determine the 95% confidence interval for the true mean strength of the beams.

Accepted Answer

490.46 MPa to 499.54 MPa

Answer

492.50 MPa to 497.50 MPa

Answer

490.00 MPa to 500.00 MPa

Answer

485.46 MPa to 504.54 MPa

Question 33

A component has a failure rate of 0.002 failures per hour. Calculate the probability of the component surviving for 1000 hours without failure.

Accepted Answer

0.1353

Answer

0.8647

Answer

0.002

Answer

0.998

Question 34

A company produces electronic components with a defect rate of 2%. Calculate the probability of finding exactly 3 defective components in a sample of 100.

Accepted Answer

0.1820

Answer

0.98

Answer

0.02

Answer

0.0004

Question 35

A bridge is designed to withstand a maximum load of 100 tonnes. The actual load on the bridge is normally distributed with a mean of 80 tonnes and a standard deviation of 10 tonnes. Determine the probability of the bridge exceeding its maximum load capacity.

Accepted Answer

0.0228

Answer

0.9772

Answer

0.0000

Answer

0.5000

Question 36

A manufacturing process produces components with a mean diameter of 10 mm and a standard deviation of 0.5 mm. Calculate the proportion of components that will have a diameter between 9.5 mm and 10.5 mm.

Accepted Answer

0.6827

Answer

0.9545

Answer

0.3413

Answer

0.1587

Question 37

A company is testing the reliability of a new type of battery. 100 batteries are tested and 5 fail within the first 100 hours of operation. Estimate the failure rate per hour.

Accepted Answer

0.0005

Answer

0.005

Answer

0.001

Answer

0.05

Question 38

A construction project has a critical path with 5 activities. The durations of each activity are estimated to be 10 days, 8 days, 12 days, 6 days, and 4 days, respectively. Calculate the expected project completion time.

Accepted Answer

40 days

Answer

20 days

Answer

50 days

Answer

30 days

Question 39

A company is producing widgets. A sample of 20 widgets is inspected, and 2 are found to be defective. Calculate the sample proportion of defective widgets.

Accepted Answer

0.1

Answer

0.02

Answer

0.2

Answer

0.5

Question 40

A machine produces bolts with a mean length of 20 mm. A sample of 10 bolts is measured, and the sample mean length is found to be 19.8 mm. Calculate the standard error of the mean.

Accepted Answer

0.2 mm

Answer

0.02 mm

Answer

2 mm

Answer

0.1 mm

Question 41

A company is using a new type of material for a product. A series of tests are conducted to determine the material's tensile strength. The results are: 50 MPa, 55 MPa, 60 MPa, 45 MPa, and 52 MPa. Calculate the mean tensile strength of the material.

Accepted Answer

52.4 MPa

Answer

50 MPa

Answer

60 MPa

Answer

55 MPa