Statistics and Probability Answers

Suppose that the thickness of a part used in a semiconductor is its critical dimension and that measurements of the thickness of a random sample of 18 such parts have the variance s2 = 0.68,
where the measurements are in thousandths of an inch. The process is considered to be under control if the variation of the thickness is given by a variance not greater than 0.36. Assuming
that the measurements constitute a random sample from a normal population, test the claim at the
α =0.05 significance level.

Compute a 95% confidence interval for the population mean, based on the numbers 1, 2, 3, 4, 5, 6, 20. Change the number 20 to 7 and recalculate the confidence interval. Using these
results, describe the effect of an outlier (i.e. extreme value) on confidence interval.

Set up a 95% confidence interval estimate for the population mean, based on each of the following sets of data, assuming that the population is normally distributed:
Set 1: 1, 1, 1, 1, 8, 8, 8, 8
Set 2: 1, 2, 3, 4, 5, 6, 7, 8
Explain why these data sets have different confidence intervals even though they have the same mean and range.

The quality control manager at a lightbulb factory needs to estimate the mean life of a large shipment of lightbulbs. The process standard deviation is known to be 100 hours. A random sample of 64 lightbulbs indicate a sample mean life of 350 hours.
a. Set up 95% confidence interval estimate of the true population mean life of lightbulbs in this shipment.
b. Do you think that manufacturer has the right to state that the lightbulbs last an average of 400 hours? Explain.
c. Does the population of lightbulbs life have to be normally distributed here? Explain.
d. Explain why an observed value of 320 hours is not unusual, even though it is outside the confidence interval you calculated.
e. Suppose that the process standard deviation changed to 80 hours. What would be your answers in (a) and (b)?

A rectangle with height and width equal to 4 and 25 respectively, is drawn on a checkered paper. Bazil paints a random horizontal 1×3 rectangle, and Peter paints a random vertical 3×1 rectangle (each rectangle consists of 3 sells). Find the probability that at least one of the cells ispainted twice. Express the answer in percent, and round to the nearest integer.

You recently received a job with a company that manufactures an automobile antitheft device. To conduct an advertising campaign for the product, you need to make a claim about the number of automobile thefts per year. Since the population of various cities in South Africa varies, you decide to use rates per 10,000 people. (The rates are based on the number of people living in the cities.) Your boss said that last year the theft rate per 10,000 people was 44 vehicles. You want to see if it has changed. The following are rates per 10,000 people for 36 randomly selected locations in the South Africa.
55 42 125 62 134 73 39 69 23 94 73 24 51 55 26 66 41 67 15 53 56 91 20 78 7025 62 115 17 36 58 56 33 75 20 16
Using this information, answer the following questions. [2.1] What hypotheses would you use ?

out of 60 applicants to a university 40 are from south, if 20 applicants are selected at random find the probability that 10 are from south

A shipment of parts contains 140 items of which 20 are defective. Two of these items
are randomly chosen and inspected. Let X denotes the defective numbers. Find the
probability distribution of X.