In a survey of 300 employees of a company regarding their 401(K) investments, th
ID: 2860829 • Letter: I
Question
In a survey of 300 employees of a company regarding their 401(K) investments, the following data were obtained.
141 had investments in stock funds.
93 had investments in bond funds.
74 had investments in money market funds.
48 had investments in stock funds and bond funds.
38 had investments in stock funds and money market funds.
37 had investments in bond funds and money market funds.
103 had investments exclusively in some other vehicle.
(a) How many of the employees surveyed had investments in all three types of funds?
employees
(b) How many of the employees had investments in stock funds only?
employees
Explanation / Answer
Answer:-
Acccording to the statement
The trick here is to see how a Venn diagram can assist you with the numbers.
It is not possible to draw one here, but set one up as follows:
4 interlocking circles for the 4 funds types, then work on other vehicle up the list
of statements from the "103 had all 4 type of fund( 3 fund +1 other investment) " -
this is the number in the centre
where the 4 circles interlock. The next 4 statements up the list allow you to
work out the numbers for where 2 circles interlock (remember that 103 of those
numbers have already been placed in the centre zone, so the numbers are ==>
103-37=66 for where bond & money market interlock
103-38=65 for where stock & money market interlock
103-48 = 55 for where stock & bond interlock
You can then use the top 3 statements to work out the numbers that are in a
single circle (set)> for stock the number is (66+65+55)-141=186-141= 45
for bond the number is 186-93=93
for money market the number is 186-74=112
lastly, work out the number that goes in the rectangle (universal set) but
not in the circles
==> (66+65+55+45+93+112+103) - 300 = 539-300 = 139
Now it is easy to answer the questions:
a:- no employ available in all three type of fund. but
(66+65+55+45+39+112) / 300 = 436 /300 = 1.45
b:- (45) / 300 = 0.15
is the required answer.
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