Why Does My Calculation of Lines Not in Use Differ from the Textbook's Answer?

In summary, a mail order business has 9 phone lines and the number of lines in use at a specified time, x, follows a pmf given in the conversation. The conversation discusses calculating the probability of certain events, specifically the probability of between two and four lines, inclusive, being not in use. The correct answer is .2, but the answer in the back of the book is .65, which is the probability of between two and four lines, exclusive, being not in use.
  • #1
maxpayne_lhp
36
0
I got a minor stuck here... please help me.

Ok the stat problem is ... a mail order business has 9 phone lines and x is the number of line in use at a specified time. pmf of X is given:

x 1 2 3 4 5 6 7
P(x) .1 .15 .2 .25 .2 .06 .04

Calculate the probability of certain events

I didn't have any problem with most events but: (e) between two and four lines, inclusive, are not in use: so would it be:
p(0) + p(5)+ p(6) = .1 +.06 + .04 = .2 ?

The answer in the back of the book is .65

What did I do wrong in here?
Thanks for yoru time and help!
 
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  • #2
No, you didn't do anything wrong. The correct answer is .2. The probability of between two and four lines, inclusive, being not in use is .2 (p(1) + p(2) + p(3) + p(4)). The probability of between two and four lines, exclusive, being not in use is .65 (p(0) + p(5) + p(6)).
 
  • #3


First of all, it's great that you are working through this problem and seeking help when you encounter difficulties. As a scientist, it's important to always seek clarification and understanding when things are not clear.

In this case, your approach is not entirely correct. To calculate the probability of between two and four lines not being in use, you need to add the probabilities of x=0, x=5, and x=6, as these values represent the number of lines not in use within the given range. So the correct calculation would be p(0) + p(5) + p(6) = .1 + .2 + .06 = .36.

The answer in the back of the book is likely taking into account the probability of x=4 as well, as this value is also within the range of two to four lines not in use. So the correct answer would be p(0) + p(4) + p(5) + p(6) = .1 + .25 + .2 + .06 = .61.

In the future, it may be helpful to double check your calculations and make sure you are considering all possible values within the given range. I hope this helps and good luck with your studies!
 

Related to Why Does My Calculation of Lines Not in Use Differ from the Textbook's Answer?

1. What is PMF?

PMF stands for Probability Mass Function, which is a concept in probability theory that describes the probability of a discrete random variable taking on a certain value. It is often used to analyze the likelihood of different outcomes in a statistical experiment.

2. What is considered a minor difficulty in PMF?

A minor difficulty in PMF can refer to a small obstacle or challenge that arises when using PMF in a statistical analysis. This could include issues such as data collection errors, small sample sizes, or unexpected outliers in the data.

3. How is PMF used in scientific research?

PMF is commonly used in scientific research to analyze and interpret data in a variety of fields such as genetics, epidemiology, and psychology. It is a useful tool for understanding the likelihood of certain outcomes and can help researchers make informed decisions based on their data.

4. What are the benefits of using PMF?

One of the main benefits of using PMF is its ability to provide a clear and concise representation of the probability distribution of a discrete random variable. This can help researchers understand the data more easily and make more accurate conclusions based on their findings.

5. Can PMF be used for continuous variables?

No, PMF is specifically used for discrete random variables, which have a finite or countable number of possible outcomes. For continuous variables, probability density functions (PDFs) are used instead.

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