Question

The mean investment that employees put into their companies 401K per year is $10,000 with a standard deviation of $500. Assuming the investments follow a normal distribution, determine the following.

a. What proportion of employees put between $9,500 and $11,000 into the 401K per year.

b. What proportion of employees put more than $11,500 into the 401K per year?

c. What proportion of employees put less than $11,000 into the 401K per year?

d. What proportion of employees put more than $9000 into the 401K per year?

e. What proportion of employees put between $11,000 and $11,500 into the 401K per Year?

Answer 1

µ = 10000

sd = 500

a)

                                                     

                                                      = P(-1 < Z < 2)

                                                      = P(Z < 2) - P(Z < -1)

                                                      = 0.9772 - 0.1587

                                                      = 0.8185

b)

                                    

                                     = P(Z > 3)

                                     = 1 - P(Z < 3)

                                     = 1 - 0.9987

                                     = 0.0013

c)

                                    

                                     = P(Z < 2)

                                     = 0.9772

d)

                                    

                                     = P(Z > -2)

                                     = 1 - P(Z < -2)

                                     = 1 - 0.0228

                                     = 0.9772

e)

                                                     

                                                      = P(2 < Z < 3)

                                                      = P(Z < 3) - P(Z < 2)

                                                      = 0.9987 - 0.9772

                                                      = 0.0215