The life of cats is normally distributed with a mean of 15 years and a standard deviation of 2 years.

Question

Find the probability of a cat living at least 10 years.

Answer 1

Prob(x>=10) = 1 - Prob(x<10) = 1 - Prob( z < (10-15)/2 )

= 1 - Prob( z<-5/2)

= 1 - Prob( z < -2.5)

= 1 - 0.00621

=0.99379

= 99.379%

This makes sense.

the mean is 15.

We seek the probability of LESS than 2.5 standard deviations BELOW the mean.

the empirical rule says the probability will be more than 95%