The lengths of a particular breed of silk moth caterpillars are generally normally distributed with a mean of approximately 7.9 cm and a standard deviation of approximately 0.42 cm. Which range of lengths represents approximately 95%of the lengths of silk moth caterpillars?
A) 7.06 cm to 8.32 cm
B) 7.06 cm to 8.74 cm
C) 7.48 cm to 8.74 cm
D) 7.48 cm to 8.32 cm
To find the range of lengths that represents approximately 95% of the lengths, we can use the empirical rule (also known as the 68-95-99.7 rule). According to this rule, approximately 95% of the data falls within 2 standard deviations of the mean.
In this case, the mean is 7.9 cm and the standard deviation is 0.42 cm.
2 standard deviations above the mean is: 7.9 + (2 * 0.42) = 7.9 + 0.84 = 8.74 cm
2 standard deviations below the mean is: 7.9 - (2 * 0.42) = 7.9 - 0.84 = 7.06 cm
Therefore, the range of lengths that represents approximately 95% of the lengths of silk moth caterpillars is approximately 7.06 cm to 8.74 cm.
The correct answer is B) 7.06 cm to 8.74 cm.