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Statistics and Probability – Q&A

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Many students face the problems when they start studying the Statistics and Probability subject. Trying to understand a lot of different aspects they feel stressed and that doesn’t have a beneficial effect on their health. Students have a great deal of statistics and probability questions that they puzzle over every day. Our service will provide every client with the statistics and probability answers. We promise to do our best to help you solve your statistics and probability problems, just let us know your problem and you will get the best statistics and probability answers ever!

The restaurant Exclusive advertises delivery of ready prepared food. The announcement states that ordered food will be served for less than 50 minutes from receiving the order. Based on a random sample of 100 orders the average time for delivery of orders is calculated to be 49 minutes, and standard deviation of 5 minutes. What can be concluded on this random sample about the time of delivery with acceptable risk ?

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Certain technological process is considered stable if the variance of a certain qualitative property is not greater than 2, otherwise the process is considered unstable. If from the sample with size 25 is obtained sample variance 1.8, what can you conclude about instability of the technological process with acceptable risk ?

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what scale of measurement is measuring statewide drug related crime rate (number of drug related arrests per 1000 individuals)

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Given a sample size of 65, with sample mean 726.2 and sample standard deviation 85.3, we perform the following hypothesis test.

Ho: μ = 750
H1: μ < 750

What is the conclusion of the test at the σ= 0.10 level? Explain your answer.

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(a) The table given below shows the nutritional and cost information for the meat (fish) and vegetable (spinach)

Per unit of fish Per unit of spinach Minimum requirement
Units of vitamins 5 1 13
Units of protein 10 3 16
Unit cost Rs. 50 Rs. 20

Find a diet (i.e. units of vitamins and proteins) to meet the minimum nutritional requirement at minimum cost.

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Mr. Fox is not the kind of person who rests. He and Batman get back to business. He is making some sort of system that gives info about the bad guys automatically.
He finds out that probability of Batman finding some criminal is 609/625 in 20 days.
But they don’t have that much time. Bane has set a deadline of 5 days to blow off the city.
What are the chances that Batman will catch Bane in 5 days and save Gotham city?

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of lost sales because of inability to supply customers.
e) A small plant with moderate demand would yield 4,500,000 annually in profits because of lost sales would be somewhat lower
f) A small plant with low demand yeld 5,500,000 annually because the plant size and market size would be matched fairly optimally.
What should ABC industries Ltd management do?

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ABC industries LTD must decide whether to build a large or small plant to produce a new product which is expected a market life of 10 years. A large plant will cost 28,000,000 to build and put into operation while a small plant will cost only 14,000,000 to build and put into operation.
The company's best estimate of the distribution of sales over the 10 years periods is:
high demand with probability = 0.5
Moderate demand with probability = 0.3
Low demand with probability = 0.2
Cost - volume profit analysis done by ABC industries Ltd management indicates these conditional outcomes under the various combinations of plant size and market size.
a) A large plant with high demand would yield 10,000,000 annually in profits.
b) A large plant with moderate demand would yield 6,000,000 annaully in profits
c) A large plant with low demand would lose 2,000,000 annaully because of productions inefficiencies.
d) A small plant with high demand would yield only 2,500,000 annually in profits considering the cost of

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Determine the test statistic (z* or t*) and the p-value for each of the following situations and Determine if they would cause the rejection of the null hypothesis if the confidence level was set at 95% in each case. (Hint: be wary of the sample size):
a) Ho: mu = 50 mL, Ha: mu "not equal to" 50 mL, sample mean = 47.3 mL, sample standard deviation= 5, n=20
b) Ho: mu "less than or equal to" 8.9 m^3, Ha: mu > 8.9 m^3, sample mean = 10 m^3, s = 3.5, n = 75
c) Ho: mu "greater than or equal to" 20^o C, Ha: mu < 20^o C , sample mean= 17.1^o C, s= 4.8^o C, n= 12
d) Ho: mu = 380 s, Ha: mu "not equal to" 380 s, sample mean = 400 s, s = 75, n = 40
e) Ho: mu = 48 units, Ha: mu "not equal to" 48 units, sample mean = 50 units, s = 9.5, n = 41

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A biologist is studying the levels of arsenic that are naturally produced in some ground water sources. A mean level of 8.0 parts per billion (ppb) and less is considered safe for agricultural use. A random sample of 40 tests of the ground water at different locations in the town of Howick yields a sample mean of 8.4 ppb with a standard deviation of 1.7 ppb. Is there enough evidence to conclude that the arsenic levels are too dangerous to use for agricultural purposes at the 98% confidence level? Conduct a complete hypothesis test which includes
a) The null and alternative hypotheses, Ho and Ha
b) The critical value (confidence coefficient)
c) The test statistic (including sample mean and standard deviation)
d) The p-value
e) A decision (do or do not accept the null hypothesis)
f) A conclusion (that refers back to the question that was posed)

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