Question

the shelf life of a particular dairy product is normally distributed with a mean of 12 days and a standard deviation of 3 days. about what percent of the products last between 12 and 15 days? 34% 2.5% 68% 16%

Explanation:

Step1: Calculate z - scores

The z - score formula is $z=\frac{x-\mu}{\sigma}$, where $\mu$ is the mean, $\sigma$ is the standard deviation, and $x$ is the value from the data set. For $\mu = 12$, $\sigma=3$, when $x = 12$, $z_1=\frac{12 - 12}{3}=0$. When $x = 15$, $z_2=\frac{15 - 12}{3}=1$.

Step2: Use the empirical rule

The empirical rule for a normal distribution states that about 68% of the data lies within 1 standard deviation of the mean ($z=- 1$ to $z = 1$). The normal distribution is symmetric about the mean. The area between $z = 0$ and $z = 1$ is half of the area between $z=-1$ and $z = 1$. So the percentage of data between $z = 0$ and $z = 1$ is $\frac{68\%}{2}=34\%$.

Answer:

34%