Statistics and Probability Answers

Use following sample home prices ($000s) to answer the questions:

175.0 48.8 995.9 298.0 218.9 209.0

628.3 111.0 212.3 2325.0 958.0 212.6

a) What is the sample median home price?

b) Do the data contain any outliers?

c) Determine variance and standard deviation.

d) Develop a Box Plot for the home prices. ]

e) Determine 8th decile.

f) Determine the coefficient of skewness using the software method.

g) In the given case, which is the better measure of Central Tendency? Why?

h) At least what percent of home prices will lie between two standard deviations of mean?

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Problem Solving

The formula for the standard error (standard deviation of the distribution of sample

means) implies that as the sample size (​n​) increases, the size of the standard error

decreases. Explain the role of the standard error in comparing the sample mean and the

population mean. Use the definitions and concepts on sample means distribution and

standard error and show examples comparing the sample mean and the population mean

of a distribution when the standard error changes in value

A certain kind of sheet metal has, on average, 9 defects per 20 square feet.

Assuming a Poisson distribution, find the probability that a 32 square foot metal sheet has at least 18 defects. Round your answer to four decimals.

8. Two identical bags each contain 12 discs, which are identical except for a) bag is selected at random and a disc is selected from it. Draw a tree diagram illustrating this situation and calculate the probability that the disc drawn will be red. b) The disc selected is returned to the same bag, along with another two the same colour, and another disc is chosen from that bag. Find the probability that i) it is the same colour as the first disc drawn ii) bag A was used, given that two discs the same colour have been chosen. 4.5 Relationships between events colour. Bag A contains 6 red and 6 blue discs. Bag B contains 8 red and 4 blue discs.

The mean value of land and buildings per acre from a sample of farms is $1600, with a standard deviation of $300. The data set has a bell-shaped distribution. Assume the number of farms in the sample is 78.

a) Estimate the number of farms whose land and building values per acre are between $1300 and $1900. 

b) What percent of the farms have a value below $1900?

A factory manufacturing light-emitting diode (LED) bulb claims that their light bulbs last for 50,000 hours on the average. To confirm if this claim was valid, a quality control manager got a sample of 50 LED bulbs and obtained a mean lifespan of 40,000 hours. The standard deviation of the manufacturing process is 1000 hours. Do you think that the claim of the manufacturer is valid? Use the 95% confidence level.

ZIMS store sells its products on installments in Karachi. The store decided to investigate the link between the life of the product and the cost. The data collected from store is shown in Table 1.1:

Table 1.1

LIFE OF PRODUCT (Years)

COST (Thousand Rupees)

3.0

25

3.5

28

4.0

32

4.5

34

5.0

34

3.0

30

5.5

40

4.5

40

4.0

42

3.5

42

6.0

50

7.5

50

8.0

53

8.5

55

a) Plot a scatter chart from the above data.

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b) Find the equation of the least square regression line in the form 𝒚 = 𝒂 + 𝒃𝒙. Given the value of 𝒂 𝑎𝑛𝑑 𝒃 up to 3 decimal places. 

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c) What are the exact interpretations of the estimated regression factors?

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d) Using your answer of part (b). Find the cost predicted by the regression line for 𝟔. 𝟓 year’s life of a product. 

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Question no 3: The average income of the residents of a particular community is your roll no *1000 and sd is your roll no *100:

What is the probability that income of a person, selected at random, is more than average income?

 What is the probability that income of a person, selected at random, is between average income and average income +2000?

What is the probability that income of a person, selected at random, is bbetween average income+1000 and average income +2000?

What is the probability that income of a person, selected at random, is less than average income +1000?

The average income of the residents of a particular community is your roll no *1000 and sd is your roll no *100:

(a) What is the probability that income of a person, selected at random, is more than average income?

(b) What is the probability that income of a person, selected at random, is between average income and average income +2000? 

(c) What is the probability that income of a person, selected at random, is bbetween average income+1000 and average income +2000?

(d) What is the probability that income of a person, selected at random, is less than average income +1000?

If X is the number obtained when a die is thrown, show that Tchebycheff's inequality gives P(|X-3.5|>2.5)<0.47. Compare this with actual probability