Question

A trader’s annual bonus is normally distributed with a mean of $650,000 and standard deviation $225,000. Her bonuses are independent from year to year. Find the probability that her average bonus over a five-year period will be less than $500,000

Answer 1

Solution :

Given that,

mean = = 650,000

standard deviation = = 225,000

n = 5

= 650,000

=  / n = 225,000 / 5=100623

P( < 500000) = P[( - ) / < (500000-650000) / 100623]

= P(z < -1.49)

Using z table  

= 0.0681   

probability= 0.0681