For each probability and percentile problem, draw the picture. The time (in years) after reaching age 60 that it takes an individual to retire is approximately exponentially distributed with a mean of about 8 years. Suppose we randomly pick one retired individual. We are interested in the time after age 60 to retirement.

40.7%

Step-by-step explanation:

The answer is linked to Poisson Distribution as probability distribution is continuous. Always remember when such kind of questions appear anywhere where the data seems to be exponentially distributed then we consider the continuous variables.

Also, Use the correct table values as well. Like in this case the table represents the value of the lesser < region. So as per the requirements of the time after the age of retirement we look for the greater region then the mean value of 8 years

                                        P(Y > 8) = 1 − P(Y ≤ 8)

See the table value:      P(Y ≤ 8)= 0.593

                                        P= 1-0.593 = 0.407

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction