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

We know that X is normally distributed, with parameters:

We need to find a score x so that the corresponding cumulative normal probability is equal to 0.95. Mathematically, x is such that:

The corresponding z score so that the cumulative standard normal probability distribution is 0.95 is

This value of zc=1.6449 can be found either with Excel, or with a normal distribution table. Hence, the X score associated with the 0.95 cumulative probability is

Graphically:

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