1. When transmitting messages from a point A to a point B, out of every 40 messages 6 need to be corrected by applying error correcting codes. What is the probability that in a batch of 200 messages sent from A to B, there will be between 38 and 42 messages that will have to be corrected.

2. The probability of an event A occurring in each of a series of independent trials is 2/3. Find the distribution function of the number of occurrences of A in 9 trials.

3. The probability that a network will be shut down on any given day is .0003. What is the probability that the network will be shut down twice in 5000 days.

4. 82% of items are "regular" and 77% of regular items are "top quality." What is the probability that a randomly picked regular item is of the top quality?

5. You have two boxes. 27 out of 30 items in the first box are "regular" and 11 out of 15 items in the second box are "regular." A randomly chosen item is taken from the second box and placed in the first. What is the probability that a randomly picked item from the first box is regular?

Solution Preview

1.
The number of messages that need to be corrected out of 200, X, follows a Normal distribution with mean 200(6/40) = 30 and variance 200(6/40)(1-6/40) = 25.5. We then need to find out

Pr(38-0.5 < X < 42+0.5)

Where we subtract and add 0.5 in the appropriate places for a continuity adjustment to the normal distribution. This calculation then becomes:

... Based on the prior and posterior probabilities given above, what is that ratio? Please see the attached file. Word Problem for probability ratio. ...

... that must occur is one because the sum of all probabilities of different ... which is why statistical theory is built on the concepts of probability. ...

Three Algebra Word Problems on Simultaneous Linear Equations. ... 3. The probability that San Francisco plays in the next Super Bowl is nine times the probability...

Statistics: Five Word Problems. ... The solution provides step by step method for the calculation of normal probability and confidence interval for mean and ...

... control over Type I error by setting the significance level. In other words, if you set it at .05, this means that you okay with the probability of rejecting ...

Solving Systems of Linear Equations and Word Problems. ... The probability that San Francisco plays in the next Super Bowl is nine times the probability that they ...

... d.greater sampling error and OX will increase 8. The mean ... a comma, and do not write any words, such as ... random sample of size two, find the probability that the ...

... to be 27.7 with an estimated standard error of 0.21 ... such a conclusion (ie explain with a few words or some ... described in part a), compute the probability that an ...