In a county containing a large number of rural homes, 60% of the homes are insured against fire. Four rural homeowners are chosen at random from this county, and x are found to be insured against fire. Find the probability distribution for x.

Step-by-step explanation:

Given

Required

The distribution of x

The above is an illustration of binomial theorem where:

This gives:

Express percentage as decimal

When x = 0, we have:

When x = 1

When x = 2

When x = 3

When x = 4

So, the probability distribution is:

First box -plot

Step-by-step explanation:

The given data set :

Arrange in order

We can see that the smallest data value = 20 and the largest date value = 32

Median = Middle most number = 24

in a box plot , both the whisker ends represents the minimum and the maximum data value. The median value is shown by the vertical line in the box.

In the given picture only first and fourth box plot showing the correct smallest and largest value to the given data set.

But the median value is correctly represented by the first one as the fourth one has median of 25.

Hence, the correct box plot for the given data : First