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Chapter 6: Problem 58

The average birth weight of elephants is 230 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 95 th percentile.

Short Answer

Expert verified
The birth weight of elephants at the 95th percentile is approximately 312.25 pounds.

Step by step solution

01

Understand the Given Values

The problem provides the following values: the mean (\u03BC) is 230 pounds and the standard deviation (\u03C3) is 50 pounds. It is also mentioned that the distribution of birth weights follows a Normal distribution.
02

Use the Z-Score Formula for Percentiles

In a Normal distribution, percentiles can be found using the Z-score formula. The Z-score for the 95th percentile (\(Z_{0.95}\)) is approximately 1.645 (this value is found in a Z-score table or can be calculated using statistical software). The Z-score formula is \(X = \u03BC + Z * \u03C3\), where X is the value at the given percentile.
03

Substitute the Known Values into the Formula

Now plug in the known values into the formula: \(X = 230 + 1.645 * 50\).
04

Solve for X

Solving the equation gives the birth weight at the 95th percentile.

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