Thirty seventh graders each took a random sample of 10 middle school students and asked each student whether or not he likes pop music. Then, they calculated the proportion of students who like pop music for each sample. The dot plot below shows the distribution of the sample proportions. Based on the dot plot, do you think the proportion of the middle school students at this school who like pop music is 0.5? Explain why or why not.

No, too many dots to the left of 0.5

And the average proportion is about 0.39, close to 0.4

Step-by-step explanation:

There are way more dots to the left of 0.5 than there are to the right of 0.5

And there are nowhere near enough dots right on 0.5 to make up for that.

So we can tell just from looking that these dots don't average out to 0.5

If you actually count the dots  and add up the values of all the dots:

1 x 0.1        =           0.1

3 x 0.2      =           0.6

9 x 0.3       =          2.7

8 x 0.4       =          3.2

6 x 0.5       =          3.0

2 x 0.6       =          1.2

1 x 0.7        =         0.7

30 proportions      11.5   Total of All Proportions

11.5/30 = 0.38333333... , a lot closer to 0.4 than to 0.5

2^y = ln 5, or   y(ln 2) = ln 5.   solving for y,   y = (ln 5) / (ln 2).   y=5

step-by-step explanation: