The Weights of Baby Elephants Distribution

What percent of baby elephants weigh more than 230 pounds? To find the percent of baby elephants weighing more than 230 pounds, calculate the z-score with the given mean and standard deviation and use it to find the corresponding probability from a standard normal distribution. Approximately 11.51% of baby elephants weigh more than 230 pounds.

Calculation and Explanation:

Normal Distribution Model: The weights of baby elephants can be modeled by a normal distribution with mean μ=200 pounds and standard deviation σ=25 pounds.

Z-Score Formula: The formula for the z-score is: Z = (X - μ) / σ

Given Values:
- X (Weight) = 230 pounds
- μ (Mean) = 200 pounds
- σ (Standard Deviation) = 25 pounds

Calculating Z-Score:
Z = (230 - 200) / 25 = 30 / 25 = 1.2

Finding Probability:
Using the z-score of 1.2, we find the probability that a baby elephant weighs more than 230 pounds. This can be done by looking up the z-score in a standard normal distribution table or using a calculator with normal distribution functions.

Result:
Without the exact value, a z-score of 1.2 typically corresponds to a cumulative probability of around 0.8849, which means approximately 11.51% of baby elephants weigh more than 230 pounds.

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