Exact Value and Approximation Refer to Figure 6-21 in Example 2, and refer to the Minitab display near the beginning of this section. Figure 6-21 shows the shaded region representing exactly 235 wins among 431 games. What is the shape of the corresponding region in the Minitab display? If we use technology without an approximation, the probability of exactly 235 wins is found to be 0.0066. If we use the normal approximation to the binomial distribution, the probability of exactly 235 wins is found from Table A-2 to be 0.0068. Which result is better? Is the approximation off by much?

Answer :

Step 1 of 1 :

Given, the shaded region representing exactly 235 wins among 431 games. The probability of exactly 235 wins is found to be 0.0066. If we use the normal approximation to the binomial distribution, the probability of exactly 235 wins is found from Table to be 0.0068

The claim is to suggest the shape of the distribution and we have to suggest the better result.

Conclusion :

The Minitab display shows that the region representing 235 wins is a rectangle.

The result of 0.0068 is an approximation, but the result of 0.0066 is better because it is based on an exact calculation. The approximation differs from the exact result by a very small amount.