Question

Two psychologists surveyed 562 children in grades 4, 5 and 6 in elementary schools in Michigan. They stratified their sample drawing roughly 1/3 from rural, 1/3 from suburban and 1/3 from urban schools. Among other questions they asked students whether their primary goal was to get good grades, to be popular, or to be good at sports. One question of interest was whether boys and girls at this age had similar goals.

	Grades	Popular	Sports	Total
Boy	108	67	89	264
Girl	151	126	33	310
Total	259	193	122	574

Round answers to two places after the decimal:

Of the boys in grades 4, 5 and 6 in elementary schools in Michigan, what proportion have as primary goal to be good at sports?

Of the girls in grades 4, 5 and 6 in elementary schools in Michigan, what proportion have as primary goal to be good at sports?

Among the students in grades 4, 5 and 6 in elementary schools in Michigan who have as primary goal to be good at sports, what is the proportion are girls?

20.

A vending machine has been known to be "finicky," that is, it will only sometimes accept dollar bills that are fed into it. Let X represent the number of bills accepted out of the last four tried.

X	0	1	2	3	4
probability	0.05	0.15	0.15	0.1	0.45

Does the table below show a correct probability model for X?

Yes, because all probabilities and all values for X are represented.

Yes, because all of the probabilities are between 0 and 1.    

No, because the sample space is missing values for X.

No, because the probabilities do not sum to 1.

Answer 1

1a)

Of the boys , proportion have as primary goal to be good at sports =89/264=0.34

b) Of the girls , proportion have as primary goal to be good at sports =33/310=0.11

c) Among the students proportion are girls given primary goal to be good at sports =(33/122)

=0.27

2)since sum of probabilities is 0.05+0.15+0.15+0.1+0.45 =0.90

No, because the probabilities do not sum to 1.