There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values. In such cases, we can use this continuity correction: Represent each whole number by the interval extending from 0.5 below the number to 0.5 above it. The Chapter Problem for Chapter 3 includes Table 3-1, which lists the numbers of chocolate chips in Chips Ahoy regular cookies. Those numbers have a distribution that is approximately normal with a mean of 24.0 chocolate chips and a standard deviation of 2.6 chocolate chips. Find the percentage of such cookies having between 20 and 30 chocolate chips inclusive.
a. Find the result without using the continuity correction.
b. Find the result using the continuity correction.
c. Does the use of the continuity correction make much of a difference in this case?