Question: 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.

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. Assume that IQ scores are all whole numbers having a distribution that is approximately normal with a mean of 100 and a standard deviation of 15.

a. Without using any correction for continuity, find the probability of randomly selecting someone with an IQ score greater than 103.

b. Using the correction for continuity, find the probability of randomly selecting someone with an IQ score greater than 103.

c. Compare the results from parts (a) and (b).

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