Question

The common fruit fly Drosophila melanogaster is the most studied organism in genetic research because it is small, easy to grow, and reproduces rapidly. The length of the thorax (where the wings and legs attach) in a population of male fruit flies is approximately Normal with mean 0.800 millimeters (mm) and standard deviation 0.078 mm. Draw a Normal curve on which this mean and standard deviation are correctly located. (Hint: Draw an unlabeled Normal curve, locate one, two and three standard deviations away from the mean, then add number labels on the horizontal axis.)

Answer 1

The Normal curve with the mean and standard deviations is shown below.

Explanation:

According to the Empirical Rule in a normal distribution with mean µ and standard-deviation σ, nearly all the data will fall within 3 standard deviations of the mean. The empirical rule can be broken into three parts:

• 68% data falls within 1 standard deviation of the mean. That is P (µ - σ ≤ X ≤ µ + σ) = 0.68.
• 95% data falls within 2 standard deviations of the mean. That is P (µ - 2σ ≤ X ≤ µ + 2σ) = 0.95.
• 99.7% data falls within 3 standard deviations of the mean. That is P (µ - 3σ ≤ X ≤ µ + 3σ) = 0.997.

The length of the thorax in a population of male fruit flies is approximately Normal.

The mean is, µ = 0.800 mm and the standard deviation is, σ = 0.078 mm.

Then:

• 68% data falls within 1 standard deviation of the mean. That is P (µ - σ ≤ X ≤ µ + σ) = P (0.722 ≤ X ≤ 0.878) = 0.68.

• 95% data falls within 2 standard deviations of the mean. That is P (µ - 2σ ≤ X ≤ µ + 2σ) = P (0.644 ≤ X ≤ 0.956) = 0.95.

• 99.7% data falls within 3 standard deviations of the mean. That is P (µ - 3σ ≤ X ≤ µ + 3σ) = P (0.566 ≤ X ≤ 1.034) = 0.997.

The Normal curve with the mean and standard deviations is shown below.