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.
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
1 answer
1 answer