a study shown that 20% of all college textbooks cost at least $70.it is known that the standard deviation of the prices of all college textbook is $9.50.assuming that prices of all college textbooks follow a normal distribution, find the mean price of all college textbooks.

http://www.jiskha.com/display.cgi?id=1369182329

Put in this applet the standard deviation, then the mean as zero.

Then start at -6, check the area. EVentually, you will get an area of .20

Then, say -6.5 is the point, you know that is really 70, so add 70 +6.5, and you have the mean.

To find the mean price of all college textbooks, we need to use the concept of the normal distribution and the given information.

Here's how we can approach the problem:

1. The problem states that 20% of all college textbooks cost at least $70. This means that the area under the normal distribution curve to the right of $70 is 20%.

2. To find the corresponding z-score for a 20% area under the curve, we can use the standard normal distribution table or a statistical calculator. The z-score is the number of standard deviations away from the mean.

3. From the standard normal distribution table, we find that the z-score corresponding to an area of 20% to the right is approximately 0.84.

4. We can use the formula for the z-score to find the mean price of all college textbooks:
z = (x - μ) / σ
where z is the z-score, x is the given value ($70), μ is the mean price, and σ is the standard deviation.

5. Rearranging the formula, we get:
μ = x - (z * σ)
Substituting the values, we have:
μ = $70 - (0.84 * $9.50)

6. Calculating the result, we get:
μ = $70 - $7.98

So, the mean price of all college textbooks is approximately $62.02.