Full Answer Section

The probability that fewer than 5 cars will fall below the average is:

(0.4)^10 = 0.000009765625

This means that there is a 0.001% chance that fewer than 5 cars will fall below the average in a random sample of 10 cars.

Probability that more than 6 cars will fall below the average

The probability that more than 6 cars will fall below the average is:

(0.6)^10 = 0.000009765625

This means that there is a 0.001% chance that more than 6 cars will fall below the average in a random sample of 10 cars.

Probability that at least 4 cars will fall below the average

The probability that at least 4 cars will fall below the average is:

1 – (0.4)^10 – (0.6)^4(0.4)^6

= 1 - 0.000009765625 - 0.021144

= 0.9788507629394531

This means that there is a 97.89% chance that at least 4 cars will fall below the average in a random sample of 10 cars.

Interpretation

The results of these calculations show that it is very unlikely that exactly 4 cars will fall below the average in a random sample of 10 cars. However, it is more likely that fewer than 5 cars will fall below the average, or that more than 6 cars will fall below the average. It is also very likely that at least 4 cars will fall below the average.

These results are consistent with the fact that the average price of the cars in the data set is $25,000. This means that half of the cars in the data set are below the average price, and half of the cars are above the average price.

It is also important to note that these results are based on a random sample of 10 cars. If we were to take another random sample of 10 cars, the results might be different. However, the probability that the results will be similar is very high.