snakes age

Question

the life span of a particular species of snake are normally distributed with a mean of 90 years and a standard deviation of 12.6. what proportion of these snakes will live between 70 and 120

Answer 1

To do this problem, you will need to

 

1.  Find the z-scores for 70 and 120

z₁ = (70 - 90)/12.6 = -1.587 ≅ -1.59

z₂ = (120 - 90)12.6 = 2.38

 

2. Calculate the probability using a Standard Normal Distribution.

Let X be the random variable representing the life span of this snake species, then the proportion of the snakes that live between 70 and 120 is

P{70 < X ≤ 120}

= P{X ≤ 120} - P{X ≤ 70}

= P{Z ≤ 2.38} - P{Z ≤ -1.59}

= 0.9913 - 0.0559

= 0.9354 or 93.54%