Statistics and Probability Answers

Question 3:
A class contains 10 men and 20 women of which half men and half women have brown eyes. Find the probability that a person chosen at random is a men or brown eyed.

Question 4:
Let A and B are two events with P(AUB)=3/4, P(A ̅ )=2/3, P(A∩B)=1/4
Find: P(A), P(B), P(A∩B ̅)
[hint: (A ̅ ) represents the compliment of event A. according to compliment law of addition P(A ̅ )=1-P(A) also P(A∩B ̅ )=P(A)-P(A∩B)]

A candy company has calibrated their machines to fill each bag of candy to an average weight of 500 grams with a standard deviation of 5 grams. The company tests the consistency of their machines by taking a sample of 25 bags and weighing them

(5 Pts) What is the probability that the average weight of candy bags in the sample is less than 498 grams?
(5 Pts) What is the probability that the sample average is between 498 and 503?
(5 Pts) Below what value do 90% of the sample means fall?

The modal interval can be determined when making a histogram and adjusting the size of the intervals.

At the University of Washington, 65% of the students have been granted a scholarship. Of the scholarship students, 80% also have a work-study job. Of students who did not receive a scholarship, 45% have a work-study job. What is the probability that a student has a scholarship and a work-study job? If a student does not have a work-study job, what is the probability that he received a scholarship?

In spite of the potential safety hazards, some people would like to have an Internet connection in their car. A preliminary survey of adult Americans has estimated this proportion to be somewhere around 0.20. Use the given preliminary estimate to determine the sample size required to estimate this proportion with a margin of error of 0.02. (Round your answer up to the nearest integer.)

Given the following normal distribution what is the probability X>35. That is, P(X>35). Assume standard deviation σ=6.

Price = 12,15,18,25,22,18,30.
Demand = 65,60,50,41,40,56,45.
Required following.
1) coefficient of correlation
2) coefficient of determination
3) probable Error
4) Interpretation

Distance =14,23,9,17,10,22,5,12,6,10. Charges= 68,105,40,79,81,95,31,72,45,93.
Required following.
1) coefficient of correlation
2) coefficient of determination
3) probable Error
4) Interpretation

In statistics testing if you obtain an alpha of 4% ,what does this mean

1.1 A batch of 5000 electric lamps has a mean life of 1000 hours and a standard deviation of 75 hours. Assuming a normal distribution: 1.1.1 how many lamps will fail before 900 hours? (5) 1.1.2 how many lamps will fail between 950 and 1000 hours? (5) 1.1.3 and given the same mean life, what would the standard deviation have to be to ensure that not more than 20% of lamps fail before 916 hours?