Question

The average birth weight of elephants is 250 pounds. Assume that the distribution of birth weights is Normal with a standard deviation of 50 pounds. Find the birth weight of elephants at the 95th percentile.

The birth weight of elephants at the 95th percentile is _______________pounds.
​(Round to the nearest integer as​ needed.)

Answer 1

The birth weight of elephants at the 95th percentile is calculated by adding the product of the 95th percentile z-score (1.645) and the standard deviation (50 pounds) to the mean weight (250 pounds), resulting in 332 pounds after rounding to the nearest integer.

Step-by-step explanation:

To find the birth weight of elephants at the 95th percentile, given that the average birth weight is 250 pounds with a standard deviation of 50 pounds, and assuming a normal distribution, we would need to use the z-score associated with the 95th percentile. The z-score for the 95th percentile is approximately 1.645. Using the z-score formula:

Z = (X - μ) / σ

where μ is the mean and σ is the standard deviation, we can rearrange the formula to solve for X (the value at the 95th percentile):

X = Z * σ + μ

Plugging in the values:

X = 1.645 * 50 + 250

X = 82.25 + 250

X = 332.25

Rounding to the nearest integer, we find that the birth weight of elephants at the 95th percentile is 332 pounds.