normal distribution

[kittiecs]

I am currently taking a class on statisics and can not figure out how to complete this problem. I am not sure of the formula to use

The price of shares of bank of Kentucky at the end of trading each day for the last year followed normal distribution. Assume there were 240 trading days in the year. The mean price was $42.00 per share and the standard deviation was $2.25 per share.

A. What percent of the days was the price over $45.00?
B. What percent of days was the price between $38.00 and $40.00
C. What was the stock's price on the highest 15 percent of days?

I am not sure how to proceed to solve this problem.
Kittie

 

[chivox]

The basic formula is

\(\displaystyle z = \frac{x - \mu}{\sigma}\)

Then, you go to the table for the z values for the normal distribution and look up z. This will tell you how much area is under the normal curve to the left (less than or equal to) that value.

Since (A) asks for the probability it's greater than some value, take 1 (total area under the curve from -infinity to +infinity = 1), minus the value you find in the table.

For (B), get the z value for those two end points and take the slice of the area under the curve between them (greater than or equal to 38 and less than or equal to 40). For example, if you find in the table that 30% of the area under the curve is to the left of $40 and 20% of the area under the curve is to the left of $38 (I doubt those are the actual numbers), then the area under the curve between $38 and $40 would be .30 - .20. If you don't follow this, follow up.

For (C), it's kind of an inverse problem. They're giving you the table lookup value. Once you look it up (1 - 15% = 0.85), solve the formula for x and plug in the z value that you got from the "reverse lookup." On the highest 15% of the days, that would be the (lowest) stock price (the question really should be worded a little more carefully). Strange question, since you don't really have the data and the normal curve is an estimate.