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, 99.7% of the cows will produce an amount of milk within which of the following ranges?

It's the probability curve of a continuous distribution that's most likely symmetric around the mean. On the Z curve, at Z=0, the chance is 50-50. A bell-shaped curve is another name for it.

The missing options are:

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

We have:

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.

The mean = 6.2 gallons

Standard deviation = 0.7 gallons

The range can be calculated:

Lower range = 6.2 - 0.7 = 5.5 gallons

Upper range = 6.2 + 0.7 = 6.9 gallons

Thus, 99.7% of the cows will produce an amount of milk in the range is 5.5 gallons to 6.9 gallons option (A) is correct.

Learn more about the normal distribution here:

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