Question 10 and 11 only A full service brokerage firm gathered information on ho

Question

Question 10 and 11 only

A full service brokerage firm gathered information on how their clients were investing for retirement. on age, clients were categorized according to where the largest percentage of their retirement portiolio was invested. The table below summarized the data. 8) Identify the variables and tell whether each is categorical or quantitative 9) Find each of the following percentages a. What percent of the clients are over age 50 who invest in mutual funds? b. What percent of clients over age 50 invest in mutual funds? c. What percent of the mutual fund investor are over age 50? 10) What is the marginal distribution of age? 11) Write a sentence or two about the conditional relative frequency distribution of mode of investment for clients age 50 or younger.

Explanation / Answer

10. from the table to find the marginal distribution of age--

there are two categories of age- 50 or younger and over age 50

so in marginal distribution we need to find the frequecny of these two categories.

so frequency of age 50 or younger is

=frequncy of age younger and mode of investment is mutual funds+frequncy of age younger and mode of investment is stocks+frequncy of age younger and mode of investment is bonds=30+37+19=86

similarly frequency of age over 50 is

=frequncy of age over 50 and mode of investment is mutual funds+frequncy of age over 50 and mode of investment is stocks+frequncy of age over 50 and mode of investment is bonds=34+45+23=102

hence the marginal distribution of age is

[answer]

11. the conditional relative frequency distribution of mode of investment for clients of age 50 or younger is= frequency of mode of investment of client with age 50 or younger/frequency of age with 50 or younger

hence the distribution is

hence from this distribution it is clear that people of age 50 or younger have done investment maximum in stocks almost 43% then in mutual funds around 35% and least in bonds 22%

these relative frequencies also represent the probabilities.

so the probability that a person has invested in mutual fund given that he/she is of age 50 or younger is 0.3488

similarly the probability that a person has invested in stocks given that he/she is of age 50 or younger is 0.4302

also the probability that a person has invested in mutual fund given that he/she is of age 50 or younger is 0.2209

age frequancy 50 or younger 86 over 50 102 total 188

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