Question

a study has shown that the daily amount of milk produced by a dairy cow is normally distributed, with a mean of 6.2 gallons and a standard deviation of 0.7 gallons. on a given day, 68% of the cows will produce an amount of milk within which of the following ranges?
a. 5.5 gallons to 6.9 gallons
b. 4.8 gallons to 7.6 gallons
c. 4.1 gallons to 8.3 gallons
d. 3.4 gallons to 9.0 gallons

Explanation:

Step1: Recall the empirical rule

For a normal distribution, approximately 68% of the data lies within 1 standard deviation of the mean, i.e., between $\mu - \sigma$ and $\mu + \sigma$.

Step2: Identify $\mu$ and $\sigma$

Given $\mu = 6.2$ gallons and $\sigma = 0.7$ gallons.

Step3: Calculate the lower and upper bounds

Lower bound: $\mu - \sigma = 6.2 - 0.7 = 5.5$ gallons.
Upper bound: $\mu + \sigma = 6.2 + 0.7 = 6.9$ gallons.

Answer:

A. 5.5 gallons to 6.9 gallons