High School

The average height of a hay crop is 37 inches with a standard deviation of 1.5 inches and is normally distributed.

Construct the normal curve using the 68-95-99.7 rule. What range of heights contains 68% of all hay crops?

A. 35.5 to 38.5 inches
B. 36.5 to 38.5 inches
C. 35.0 to 39.5 inches
D. 35.5 to 39.0 inches

Answer :

Final answer:

The range of heights that contains 68% of all hay crops is 35.5 to 38.5 inches, found by applying the 68-95-99.7 rule and calculating one standard deviation above and below the mean. Therefore correct option is B

Explanation:

The range of heights containing 68% of all hay crops, based on the average height of a hay crop which is 37 inches with a standard deviation of 1.5 inches, can be found using the 68-95-99.7 rule for a normal distribution. This rule states that approximately 68% of the data will fall within one standard deviation of the mean.

Therefore, to find the range we add and subtract one standard deviation (1.5 inches) from the mean (37 inches).

The calculation would be:
Lower limit: 37 - 1.5 = 35.5 inches
Upper limit: 37 + 1.5 = 38.5 inches

Thus, the range of heights that contains 68% of all hay crops is 35.5 to 38.5 inches (Option B).