Question

The weights of baby elephants can be modeled by a normal distribution with mean μ=200 pounds and standard deviation σ=25 pounds. Use the empirical rule to estimate the proportion of baby elephants weigh less than 150 pounds.

Answer 1

Using the empirical rule, since 150 pounds is two standard deviations below the mean of 200 pounds, we estimate that approximately 2.5% of baby elephants weigh less than 150 pounds.

Step-by-step explanation:

The question asks us to use the empirical rule to estimate the proportion of baby elephants that weigh less than 150 pounds, given that the weights are normally distributed with a mean (μ) of 200 pounds and a standard deviation (σ) of 25 pounds.

According to the empirical rule (or 68-95-99.7 rule), for a normal distribution:

• Approximately 68% of the data falls within one standard deviation of the mean.
• Approximately 95% of the data falls within two standard deviations of the mean.
• Approximately 99.7% of the data falls within three standard deviations of the mean.

To find the proportion of baby elephants that weigh less than 150 pounds, we calculate how many standard deviations 150 is from the mean:

150 pounds is 50 pounds less than the mean of 200 pounds, which is 2 standard deviations below the mean (50 pounds / 25 pounds per standard deviation = 2).

So, using the empirical rule, approximately 2.5% of the data falls below the mean minus two standard deviations. Therefore, we estimate that about 2.5% of baby elephants weigh less than 150 pounds.