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Baby chickens have a mean weight gain of 6.1 ounces in their first two weeks of life. The standard deviation of the weight gains is 0.4 ounces. Which interval below will contain almost all of the various weight gains by baby chickens after two weeks?

(1) 4.9 to 6.2 ounces
(2) 5.7 to 6.5 ounces
(3) 6.1 to 7.5 ounces
(4) 5.3 to 6.9 ounces

1 Answer

4 votes

Final answer:

Using the empirical rule, the interval that will contain almost all of the various weight gains by baby chickens after two weeks is 4.9 to 7.3 ounces. The closest provided option is (4) 5.3 to 6.9 ounces.

Step-by-step explanation:

To determine which interval will contain almost all of the various weight gains by baby chickens after two weeks, we can use the empirical rule which states that almost all (approximately 99.7%) of the data for a normally distributed set lie within three standard deviations from the mean. Here, the mean weight gain is 6.1 ounces, and the standard deviation is 0.4 ounces.

Calculating the range within three standard deviations from the mean gives us:

Lower limit = Mean - (3 × Standard deviation)
= 6.1 ounces - (3 × 0.4 ounces)
= 6.1 ounces - 1.2 ounces
= 4.9 ounces

Upper limit = Mean + (3 × Standard deviation)
= 6.1 ounces + (3 × 0.4 ounces)
= 6.1 ounces + 1.2 ounces
= 7.3 ounces

Therefore, the interval that will contain almost all of the various weight gains by baby chickens after two weeks is 4.9 to 7.3 ounces. Out of the provided options, the interval that is closest to our calculated range and might contain almost all the weights based on the empirical rule is (4) 5.3 to 6.9 ounces.

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