Exhibit 6-6.Let the lifetime of a new Jet Ski be represented by a lognormal variable, where X is normally distributed.Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. Refer to Exhibit 6-6.What proportion of the Jet Skis will last nine or more years?
A)0.1379
B)0.1587
C)0.8413
D)0.8621

Question

Exhibit 6-6.Let the lifetime of a new Jet Ski be represented by a lognormal variable,  where X is normally distributed.Let the mean of the lifetime of the Jet Ski be six years with a standard deviation of three years. Refer to Exhibit 6-6.What proportion of the Jet Skis will last nine or more years?
A)0.1379 
B)0.1587 
C)0.8413 
D)0.8621

Quizplus · Accepted Answer

We need to find P(X≥9).
First, we need to standardize the value using the formula z = (ln(9)-μ)/σ, where μ = mean and σ = standard deviation.
z = (ln(9)-6)/3 = 0.4621
Using a standard normal table or calculator, we find the area to the right of z= 0.4621 is 0.1379.
Therefore, the proportion of Jet Skis that will last nine or more years is 0.1379 or 13.79%. Option A is the correct choice.