Statistics problems dealing with probability
Not what you're looking for?
1. All Seasons Plumbing has two service trucks which frequently break down. If the probability the first truck is available is .75, the probability the second truck is available is .50, and the probability that both trucks are available is .30, what is the probability neither truck is available?
2. Textbook authors and publishers work very hard to minimize the number of errors in a text. However, some errors are unavoidable. Mr. J. A. Carmen, statistics editor, reports that the mean number of errors per chapter is 0.8. What is the probability that there are less than 2 errors in a particular chapter?
3. A recent issue of Bride Magazine suggested that couples planning their wedding should expect two-thirds of those who are sent an invitation to respond that they will attend. Rich and Stacy are planning to be married later this year. They plan to send 197 invitations.
a) How many guests would you expect to accept the invitation?
b) What is the standard deviation?
c) What is the probability 140 or more will accept the invitation?
d) What is the probability exactly 140 will accept the invitation?
4. A processor of carrots cuts the green top off each carrot, washes the carrots, and inserts six to a package. Twenty packages are inserted in a box for shipment. To test the weight of the boxes, a few were checked. The mean weight was 20.4 pounds, the standard deviation 0.5 pounds. How many boxes must the processor sample to be 95 percent confident that the sample mean does not differ from the population mean by more than 0.2 pounds?
Purchase this Solution
Solution Summary
This solution gives a clear, detailed explanation of how to accurately solve four statistics problems, all of which concern probability. The expert provides both calculations and equations, as well as a text explanation of how to achieve the answer.
Solution Preview
1. Denote by A the event that the first truck was available, and denote B by the event that the second truck is available. We know that P(A) = 0.75 and P(B) = 0.5, P(AB) = 0.3.
So, P(P U B) = P(A) + P(B) - P(AB) = 0.75 + 0.5 - 0.3 = 0.95
So, P(barA bar B) = 1 - P(A U B) = 1 - 0.95 = 0.05
So, the probability neither truck is available is 0.05.
2. We assume that the number of errors X in a text follows Poisson distribution, namely:
P(X=k) = (1/k!)*e^-λ*(λ^k),k = 0,1,2,3,...
By given ...
Education
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
Recent Feedback
- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
- "excellent work"
- "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
- "Thank you"
- "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Know Your Statistical Concepts
Each question is a choice-summary multiple choice question that presents you with a statistical concept and then 4 numbered statements. You must decide which (if any) of the numbered statements is/are true as they relate to the statistical concept.
Measures of Central Tendency
Tests knowledge of the three main measures of central tendency, including some simple calculation questions.
Terms and Definitions for Statistics
This quiz covers basic terms and definitions of statistics.
Measures of Central Tendency
This quiz evaluates the students understanding of the measures of central tendency seen in statistics. This quiz is specifically designed to incorporate the measures of central tendency as they relate to psychological research.