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:

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

Venn Diagram, binomial probability problems. ... B). (c) Sketch a Venn diagram and describe it in words. ... The probability of winning from a single bottle purchase was ...

... can be used to obtain the answers of similar problems. ... In other words, a perfectly competitive firm has no control ... a. What is the probability that no more than ...

... The Attached word document contains solutions to problems including ... From the table, the probabilities for a Z ... The probability, for a value lying between 450 and ...

I'm having trouble writing equations for word problems. ... die is weighted so that the probabilities of rolling ... 4,5, or 6 are equal and the probability of rolling ...

... III. Formulation and wording of the questions - The wording and the ... "Probability Sampling ... The response address the queries posted in 1700 words with references. ...

... So the answer is 0.9 or 90% probability that San Francisco will play in the Super ... Solution: We'll form the following equation from the given worded problem: ...

... Solution attached as a *WORD* document ... sampling distribution of the sample mean is the probability distribution of ... In your own words, describe the units in this ...

Normal Probabilities and Confidence Interval. ...problems should be submitted via the Drop Box as a single Word document with ... Using the Normal_ Probability.xls file ...

... type: empirical probability and theoretical (classical) probability. Explain clearly how these probabilities are used. I have to admit that the wording to your ...