the weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a…

the weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a standard deviation of 1.5 oz. using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard.

the weight of oranges growing in an orchard is normally distributed with a mean weight of 8 oz. and a standard deviation of 1.5 oz. using the empirical rule, determine what interval would represent weights of the middle 99.7% of all oranges from this orchard.

Answer

Explanation:

Step1: Recall the empirical rule

The empirical rule for a normal distribution states that about 99.7% of the data lies within 3 standard - deviations of the mean.

Step2: Calculate the lower bound

The formula for the lower bound $L$ is $L=\mu - 3\sigma$, where $\mu$ is the mean and $\sigma$ is the standard deviation. Given $\mu = 8$ oz and $\sigma=1.5$ oz, then $L = 8-3\times1.5=8 - 4.5 = 3.5$ oz.

Step3: Calculate the upper bound

The formula for the upper bound $U$ is $U=\mu + 3\sigma$. So $U = 8+3\times1.5=8 + 4.5 = 12.5$ oz.

Answer:

The interval is $(3.5,12.5)$ oz.