Question

1. the weight of oranges growing in an orchard is normally distributed with a mean weight of 5.5 oz. and a standard deviation of 0.5 oz. using the empirical rule, what percentage of the oranges from the orchard weigh between 5 oz. and 6 oz.?

options: 68%, 65%, 95%, 99.7%

Explanation:

Step1: Identify mean and standard deviation

Mean ($\mu$) = 5.5 oz, Standard Deviation ($\sigma$) = 0.5 oz.

Step2: Find how many standard deviations from mean

For 5 oz: $5 = 5.5 - 0.5 = \mu - \sigma$
For 6 oz: $6 = 5.5 + 0.5 = \mu + \sigma$

Step3: Apply Empirical Rule

Empirical Rule states that for normal distribution, about 68% of data lies within $\mu \pm \sigma$.

Answer:

68% (corresponding to the option with "68%")