The retail price of 12-pack soda can be characterized as having a normal distribution with a mean of 3.05 dollars and a standard deviation of 0.24. Below what price do you find 40 percent of all 12-packs?
Z = (score-mean)/SD
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability (.40) and its Z score. Insert data into equation above and solve.
To find the price below which you can find 40 percent of all 12-packs, you need to determine the z-score corresponding to the 40th percentile. The z-score tells you the number of standard deviations a value is away from the mean in a normal distribution.
To calculate the z-score, you can use the formula:
z = (x - μ) / σ
Where:
z = the z-score
x = the value you want to find the percentile for
μ = the mean of the distribution
σ = the standard deviation of the distribution
In this case,
x = unknown
μ = 3.05 dollars
σ = 0.24
Since you want to find the price below which 40 percent of all 12-packs fall, you are looking for the value corresponding to the 40th percentile. In a standard normal distribution, the 40th percentile is -0.25.
So, rearranging the formula, we have:
-0.25 = (x - 3.05) / 0.24
Now, you can solve for x.
-0.25 * 0.24 = x - 3.05
-0.06 = x - 3.05
x = -0.06 + 3.05
x ≈ 2.99
Therefore, the price below which you can find 40 percent of all 12-packs is approximately $2.99.