Final answer:
The percentage of corn that falls between 2.2 m and 3.7 m in height is approximately 95%, according to the empirical rule and the given normal distribution of corn heights. The correct option is C.
Step-by-step explanation:
Normal Distribution and the Empirical Rule:
Given the parameters for the variation in corn height, we can use the empirical rule to determine the percentage of corn heights that fall within the range of 2.2 m to 3.7 m. The empirical rule states that for a normal distribution, roughly 68% of the data will fall within one standard deviation of the mean, 95% within two standard deviations, and 99.7% within three standard deviations.
In this scenario, the mean height for the corn is 2.7 m, and the standard deviation is 0.5 m. We are interested in the percentage of corn between 2.2 m and 3.7 m. Calculating the number of standard deviations each value is from the mean:
- 2.2 m is 1 standard deviation below the mean (2.7 - 0.5 = 2.2)
- 3.7 m is 2 standard deviations above the mean (2.7 + 2(0.5) = 3.7)
According to the empirical rule, approximately 68% of the data lies within one standard deviation of the mean, and approximately 95% lies within two standard deviations. Since 3.7 m is within two standard deviations above the mean, and 2.2 m is within one standard deviation below, the percentage we seek is likely to be slightly less than 95% but considerably more than 68%.
For simplicity, the exact percentage can often be found using statistical tables or calculators with the normal distribution function, but based on the options provided, the closest answer without these resources is approximately 95% (Option C). This is because we are looking at a range that covers from one standard deviation below to two standard deviations above the mean.