Question

question 8 of 10
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, 95% 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 normal distribution

For a normal distribution, approximately 95% of the data lies within \( \mu\pm2\sigma\), where \(\mu\) is the mean and \(\sigma\) is the standard deviation.

Step2: Calculate the lower and upper bounds

Given \(\mu = 6.2\) gallons and \(\sigma=0.7\) gallons.
The lower bound is \( \mu - 2\sigma=6.2-2\times0.7\)
\(=6.2 - 1.4=4.8\) gallons.
The upper bound is \( \mu + 2\sigma=6.2 + 2\times0.7\)
\(=6.2+1.4 = 7.6\) gallons.

Answer:

B. 4.8 gallons to 7.6 gallons