the weight of oranges growing in an orchard is normally distributed with a mean weight of 4.5 oz. and a…

the weight of oranges growing in an orchard is normally distributed with a mean weight of 4.5 oz. and a standard deviation of 0.5 oz. using the empirical rule, what percentage of the oranges from the orchard weigh between 3 oz. and 6 oz.?

the weight of oranges growing in an orchard is normally distributed with a mean weight of 4.5 oz. and a standard deviation of 0.5 oz. using the empirical rule, what percentage of the oranges from the orchard weigh between 3 oz. and 6 oz.?

Answer

Answer:

99.7%

Explanation:

Step1: Calculate number of standard - deviations from the mean

For the lower value: $z_1=\frac{3 - 4.5}{0.5}=\frac{- 1.5}{0.5}=-3$ For the upper value: $z_2=\frac{6 - 4.5}{0.5}=\frac{1.5}{0.5}=3$

Step2: Apply the empirical rule

The empirical rule for a normal distribution states that approximately 99.7% of the data lies within 3 standard - deviations of the mean. Since the values 3 oz. and 6 oz. are 3 standard - deviations below and above the mean respectively, the percentage of oranges that weigh between 3 oz. and 6 oz. is 99.7%.