Statistics Sheet 8 questions

Exam #1 (covers chapters 1-5), Math 140

Spring 2015, CSUN Show All Work! Name:___________________________

Seat Number:_____________________ Papers without name/seat number would lose 10 points. Write your name and seat number now. You must show all work for full credit. 1) Define the following term: Stratified Random Sample. (6 points)

2) The amount of cash (rounded to whole dollars) carried by each student in a simple random sample of CSUN’s

students who take MWF classes are given below: 3, 5, 8, 11, 4, 11, 9, 6, 9, 21, 24, 32, 23, 18, 25, 17, 2, 1, 30, 15, 27, 28, 32, 16, 20, 8, 5, 2, 20, 15.

A) Construct a relative frequency distribution table, with the first class having a lower class limit of 1 and a class width of 6. (8 points) B) Construct a relative cumulative frequency distribution related to part (A). (4 points) C) Construct a histogram and a pie chart for the data set in part A, use relative frequency for both graphs. (8 points)

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3) The average distance of students living away from campus is 10 miles. If the standard deviation is 2.5 miles, what are the z-scores for two students who live 14 and 20 miles away from campus? Are these z-scores usual or unusual? Explain why or why not. (8 points)

4) The following frequency distribution shows the ages of the employees working in a movie production company

in Hollywood. Treating these data as a sample of employees in movie industry, A) compute the mean, and standard deviation. Comment on age distribution of the employees. Explain. (12 points) Age Frequency 20 - 24 11 25 - 29 19 30 - 34 25 35 - 39 20 40 - 44 10

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5) Find the 5-number summary for the data: 2, 8, 5, 10, 15, 9, 21, 32, 17, 18, 24, 43, 28, 20. Indicate any outliers by calculating upper and lower fences and mark all these information on a boxplot. (16 points)

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6) Let X be the number children with green eyes in a family of four children whose one of their parents has green eyes. Is the following a probability distribution? If yes, then find its mean and standard deviation. If not, explain why not. (13 points)

X P(X) 0 0.35 1 0.25 2 0.20 3 0.15 4 0.05

7) A family has three children, find the probability of having at least two boys. Write the sample space, first. (10

points)

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8) A recent survey indicates that 55% of adults ages 40-49 live alone. A) If we randomly select 10 adults from that age group, what is the probability that at least one of them lives alone? B) Is it unusual to randomly select 10 adults from that age group to find that at least 1 of them lives alone? Why or why not? C) Find mean and standard deviation when n is 10 and p = 0.55. (15 points)

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x = Σx n

mean,

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x = Σf ⋅ x Σf

mean (freq. table),

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s = Σ(x − x )2

n −1 standard deviation,

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s = n(Σx2)−(Σx)2

n(n −1)

standard deviation (shortcut),

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s = n(Σf ⋅ x2)−(Σf ⋅ x)2

n(n −1) standard deviation (freq table), variance =

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s2,

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z = x − x

s Standard score (sample),

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z = x − µ σ

Standard score (population),

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IQR = Q3 −Q1,

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LF = Q1 −1.5* IQR

lower fence ,

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UF = Q3 +1.5* IQR upper fence,

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µ = ΣxP(x) Mean (prob. dist.),

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σ = Σx2P(x)− µ2 Standard

deviation (prob. dist.),

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P(x) = (nCx)pxqn−x = n!

x!(n − x)! pxqn−x binomial probability,

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µ = np Mean (binomial),

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σ = npq Standard deviation (binomial)