6/23/2019 Chapter 6 Exploring Statistics We b A ssi g n ...

6/23/2019

Chapter 6 Exploring Statistics

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Chapter 6 Exploring Statistics (Homework)

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Due : Wednesday, June 26, 2019 11:59 PM EDTLast Saved : n/a Saving... ()

1. ?/1 pointsASWESBE9 6.AQ.502a.

Use the applet "Useful zscores of the Normal Distribution" to answer the following questions.

(a) What probability range is associated with z = ?1.96?

90% 95% 99% 99.9%

(b) What is the zvalue for a onetail (upper) probability of 5%? 1.65 1.96 2.33 3.29

P obability & Data Analysis

2. ?/1 pointsASWESBE9 6.AQ.502b.

Use the applet "Probabilities for the Standard Normal Distribution using Text Boxes (Lower Tail)" to answer the following questions. (a) What is the zscore for an uppertail probability of 0.10?

-1.96 1.645 1.282 -2.33

(b) What is the probability for the region -1.75 z 1.5? 0.973 0.893 0.613 0.586



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Chapter 6 Exploring Statistics

3. ?/1 pointsASWESBE9 6.AQ.502c.

Use the applet "Standard Normal Probability Ranges" to answer the following questions. (a) What is the probability for the region -1.00 z 1.00?

0.6833 0.8413 0.3432 0.1587

(b) What zvalue relates to a lowertail probability of 1%? 2.32 1.96 -1.96 -2.32



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6/23/2019

Chapter 6.1 Homework

1. ?/1 pointsASWESBE9 6.E.002.MI.

The random variable x is known to be uniformly distributed between 10 and 20. (a) Show the graph of the probability density function.

(b) Compute P(x < 15). (c) Compute P(13 x 15). (d) Compute E(x). (e) Compute Var(x). (Round your answer to two decimal places.)



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Chapter 6.1 Homework

2. ?/1 pointsASWESBE9 6.E.004.

Most computer languages include a function that can be used to generate random numbers. In Excel, the RAND function can be used to generate random numbers between 0 and 1. If we let x denote a random number generated using RAND, then x is a continuous random variable with the following probability density function.

f(x) = 1 for 0 x 1 0 elsewhere

(a) Graph the probability density function.

(b) What is the probability of generating a random number between 0.35 and 0.85? (c) What is the probability of generating a random number with a value less than or equal to 0.30? (d) What is the probability of generating a random number with a value greater than 0.80? (e) Generate 50 random numbers by entering =RAND() into 50 cells of an Excel worksheet.



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Chapter 6.1 Homework

This answer has not been graded yet. (f) Compute the mean and standard deviation for the random numbers in part (e).

This answer has not been graded yet.

3. ?/1 pointsASWESBE9 6.E.007.

Suppose we are interested in bidding on a piece of land and we know one other bidder is interested. The seller announced that the highest bid in excess of $20,000 will be accepted. Assume that the competitor's bid x is a random variable that is uniformly distributed between $20,000 and $25,000.

(a) Suppose you bid $21,000. What is the probability that your bid will be accepted?

(b) Suppose you bid $24,000. What is the probability that your bid will be accepted?

(c) What amount should you bid in dollars to maximize the probability that you get the property? $

(d) Suppose you know someone who is willing to pay you $26,000 for the property. What is the expected profit in dollars if you bid the amount given in part (c)? $ Find a bid in dollars which produces a greater expected profit than bidding the amount given in part (c). (If an answer does not exist, enter DNE.) $ Would you consider bidding less than the amount in part (c)? Why or why not? Yes. There is a bid which gives a greater expected profit than the bid given in part (c), and thus a higher expected profit is possible with a bid smaller than the amount in part (c). No. The bid which maximizes the expected profit is the amount given in part (c), thus it does not make sense to place a smaller bid.

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