NDE 631 Advanced NDE

ASSIGNMENT 1: Questions on Probability, Statistics, and POD

1. The probability of rain tomorrow is .30, and the probability of all members of ECN 215

being present in class is .6 (let us say). What is the probability of both these events occurring?

2. For each of the following pairs, state whether you think the events are statistically

independent or not. Explain briefly.

1. Disposable income and consumption in the US.

2. Consumption in the US and GNP in Britain.

3. Rainfall and the rate of inflation.

4. Rainfall and the price of corn.

5. An individual's shoe size and her height.

6. An individual's shoe size and her income.

Suppose that IITM students have a mean height of 68 inches, with a standard deviation of 3

inches. If heights are normally distributed, what is the probability that a randomly-selected

IITM Student is between 63 and 73 inches tall? Also, a student X, who is not aware of the

above information, intends to draw a random sample of 50 students in order to estimate the

population mean height. What is the probability that the sample mean height she obtains lies

between 63 and 73 inches?, Also, Can you think of any reason why the heights of IITM

students might not follow the normal distribution?

You are trying to estimate the average household income in Chennai. You randomly sample

200 households, and come up with the following sample statistics: mean = INR 28000,

standard deviation = INR 5000. Draw up the 95 per cent confidence interval for your estimate

of the population mean income. Give a brief interpretation of your answer.

A researcher is experimenting with several regression equations. Unknown to him, all of his

formulations are in fact worthless, but nonetheless there is a 5 per cent chance that each

regression will--by the luck of the draw--appear to come up with `significant' results. Call

such an event a `success'. If the researcher tries 10 equations, what is the probability that he

has exactly one success? What is the probability of at least one success?

Quality control requires that Phillips light bulbs have an average life of 1000 hours, with a

standard deviation of no more than 20 hours. Each month, a sample of 50 bulbs is tested to

see whether current production is meeting the standard. If a statistically significant deviation

from 1000 hours mean life is found, the production process must be inspected for faults. In

this context, `statistically significant' is taken to mean that the probability that the observed

deviation of the sample mean from 1000 is due to chance alone is 10 per cent or less. This

month the sample mean life turns out to be 996 hours. What is the probability that this

deviation from 1000 is just due to sampling error? Does this sample call for inspection of the

production process?

For a Voltage signal of mean strength of 5 V and Std Dev of 1 V, it was determined that the

noise levels are also normally distributed at a mean of 2 V and a SD of 1 V. Can you draw

the curves for the distribution and provide insight on how to determine the probability of

detection of a flaw that is expected to have a response signal of 4 V?