Question

A drawer contains black socks and white socks. 70% of the socks are black socks. A

number generator simulates randomly selecting 10 socks from the drawer. The
number generator is used 10 times and the number of black socks in each trial is
shown in the dot plot.
0 1 2 3 4 5 6 7 8 9 10
Which description is correct about the number generator being fair or not?
The number generator is not fair.

The correct percentage of black socks was not
chosen at all.

The number generator is fair. It picked the approximate percentage of black
socks most of the time.

The number generator is not fair. In three experiments, it picked black socks less
than 50% of the time.

The number generator is fair. It only picked black socks half of the time.

Answer 1

Based on the given information, it is not possible to definitively determine whether the number generator is fair or not. However, we can make some observations and inferences:

We know that 70% of the socks in the drawer are black, which means that in a random selection of 10 socks, we would expect to see around 7 black socks on average.

The dot plot shows the number of black socks in 10 trials of the number generator. We can see that the number of black socks varies from 0 to 10, with some frequencies being higher than others.

Without knowing the exact frequencies or probabilities, we can see that the dot plot does not appear to be centered around 7 black socks, which is what we would expect from a fair number generator. However, it is difficult to determine whether the deviations from 7 are statistically significant or not, without more information.

Therefore, based on the given information, the most accurate statement is:

The number generator's fairness cannot be determined with certainty from the given data, but there are indications that it may not be perfectly fair.

Explanation: