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Part II Practice Problems on Probability,
The Basis for Inferential Statistics
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Problem Answers

1.   The probability of someone not paying their overdue account follows a binomial distribution with a mean of 10%. Using a table, state the distribution, graph it, and answer answer the following questions concerning 4 overdue accounts recently encouraged to pay their overdue account. Where applicable, show all arithmetic.

Hint: x is the number of accounts not paid.

A) and B)









C) What is the probability that:

1) no one will pay

2) all will pay

3) at least two will not pay

 

 

 

 

 

3. Mistakes made by data entry clerks follows a Poisson distribution with a mean 0.8 per hour. You just gave someone applying for your data entry vacancy an hours worth of data entry material. Answer the following questions. Where applicable, show all arithmetic.

A) What is the probability they will not make any mistakes?





B) What is the probability they will make at least three mistakes?





C) What is the probability they will make less than or equal to two mistakes?



D) Questions B and C are ______________________ .



E) What is the probability they will not make as many as 4 mistakes?

 

 

 

Assume that average points scored by an NBA player is normally distributed with a mean of 15 points and a standard deviation of 4 points. Answer the following questions being sure you draw and label a graph and enter the data into an equation or expression.

A) Five percent of the players score less than _____ points.







B) A player scoring at least 10 points _____ percent of the time.







C) The interquartile range is between _____ and _____ points.









D) A player scoring between fifteen and twenty points ______ percent of the time.







E) What is the probability of a player scoring more than twenty-six points?

 

Answer _____

F) The eighth decile is between _____ and _____.





G) How often does a player score at least twenty points but not as many as thirty points?

 



4.  Quick Access.com is planning to give away software to access the internet provided customers will sign up for a reasonable period of time . A sample of 36 customers from their target market had a mean contract time of 16 months and a standard deviation of 2 months. Calculate the 99% confidence interval for the mean of the targeted population.







5A  This problem is extra credit for Franklin Pierce College students. Using expression VIII B on page 77, calculate the 95% confidence interval for the percentage of defective parts based on a sample proportion of defective parts equal to .04 from a sample of 100.


.






5B.  Redo 5A with a 99% confidence interval and analyze the results.











6.  Using two or more paragraphs consisting of complete sentences, explain why taking a sample may be more appropriate than taking a census.







7.   Using two or more paragraphs consisting of complete sentences, give two examples of experiments that may follow a binomial distribution and two that may follow a Poisson distribution.

 

 

 

 

 

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Problem Answers

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1A) x P(x) 1B) The graph of this discrete should have values from 0 to 3 on the x-axis and probabilities from 0% to about 70% on the y-axis.
0 0.656
1 0.292
2 0.049
3 0.004
4 0.000
C1) 0.0 C2) 0.656 C3) 0.049 + 0.004 = 0.053
2) A) 0.4493 B) 0.0383 + 0.0077 + 0.0012 + 0.0002 = 0.0474 C) 0.4493 + 0.3595 + 0.1438 = 0.9526 D) complements E) 0.4493 + 0.3595 + 0.1438 + 0.0383 = 0.9909
3) A) 15 - 6.58 = 8.42 B) 0.3944 + 0.5000 = 0.8944 C) 12.32 to 17.68 D) 0.3944 E) 0.5000 - 0.4970 = 0.0030 F) 17.08 to 18.36 G) .4989 - .3944 = .010.45
4) 15.14 months to 16.84 months
5) A) Using a 95% confidence interval, the percentages of defects for this population is 0.0016 to 0.0784 B) Using a z of 2.575, the range of -.010 to .090 for the 99% confidence interval is not possible because a defects percentage can not be negative. A larger sample must be taken in hopes of lowering the standard error so a negative answer is not possible.
6) See page 66.
7) See problems on pages 52 to 57 and page 81.

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