Probability

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Probability
Message posted by Linda (via 152.163.201.178) on June 6, 2001 at 3:52 AM (ET)

Stwart has observed that the daily revenues for his store follow an approximately normal distribution with mean=$550 and Standard deviation=$175

1) find the probability that the revenues for a day chosen at random will be between $500 and $600

2) Stuart has determined that to make a profit he must take in revenues of at least $675. What is the probability that he will make a profit?

3) Determine the probability that the sample mean revenues for a random sample of 49 days will be between $500 and $575.

4) To "break even", Stuart has to decide that no more than 10% of his daily revenues can be below a certain value. Find this "cut off" number

READERS RESPOND:
(In chronological order. Most recent at the bottom.)

Re: Probability
Message posted by nancy diehl (via 129.176.151.122) on June 6, 2001 at 2:09 PM (ET)

This problem is a direct application of figuring area under the normal curve; translating your raw data values into Z values and then looking that Z value up in the table. You are given all the information for you to do this.
1. It's helpful if you draw yourself a normal bell shaped curve, drop a line in the center and mark that as 550. Drop another line about where 500 and 600 would be. Now shade in this area so you can visualize the probability, or area under the curve you need to find. Now convert 500 to a Z value {(500-550)/175}, then find the area under the curve associated with this Z value and then do the same for 600. Add these two areas together and that's your probability.
2. Same method here. Again, it helps to draw a line in the curve to see where 675 would fall and shade in the area of interest (in this case it's the area to the right of 675). Convert 675 to a Z value as described above, and find it's area in the table.
3. Now you are dealing with means so the formula for Z changes slightly from the denominator being s (stddev) to the denominator being s/SQRT(n) because you need to use the std error of the mean, not the stddev of the raw data. Again, convert 500 &575 to Z values using the formula above with the different denominator.
4. Now you are given the area under the curve (left tail) to be 10%. You need to find the Z value associated with 10% of the area in the tail of the distribution. Then using the mean and stdev, you are looking for the value of X with that certain Z value. Plug in all your knowns and solve for the one unknown.

NOTE: Be careful to note the Ztable you are using. There are different ones out there. Some report the tail areas under the curve for certain Zs, others provide the area between the Zvalue and the mean. Both are correct, you just have to make sure you match what you are looking for with what is given in the table (i.e. you may need to subtract .5 from the area if you are looking for a tail area)

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