Question

1. It is estimated that the weight of a population of brown bears is approximately

normally distributed with a mean of 600 pounds and a standard deviation of 120
pounds. Approximately what proportion of the bears in the population weigh less
than 720 pounds? *

Answer 1

There are 84.13% bears with less than 720 pounds

Explanation:

The normal curve or bell curve is a bell shaped function that represents the distribuition of values around a certain mean, where the standard deviation represents the spread of the function. Values from the mean to one standard deviation represent 34.13% of all the values, from the mean to two standard deviation represents 47.73% of all the values, from the mean to three standard deviation represents 49.86% of all the values and finally from the mean to the end of the distribuition there are 50% of all the values. The distribuition is symmetric, therefore the same applies to the other side.

In this problem we want to know how many bears weigh less than 720 pounds, the mean is 600 pounds and the standard deviation is 120 pounds, therefore we want to know how many bears have a weigth that is less than the mean plus one standard deviation. Since from the mean to the tail of the distribution there are 50% of the values and from the ean from 1 standard deviation there are 34.13 % of all the values, then there are 84.13% bears with less than 720 pounds.