Chapter 6 - The Normal Distribution - 6-4 The Normal Approximation to the Binomial Distribution - Exercises 6-4 - Page 360: 8

a. Yes, b. Yes, c. No. Please see explanations below.

We need to check if the following conditions are satisfied: $np≥5$ and $nq≥5$ a. $np=10>5$ and $nq=n(1−p)=40>5$, so it can be approximated by a normal distribution. b. $np=24>5$ and $nq=n(1−p)=6>5$, so it can be approximated by a normal distribution. c. $np=17>5$ and $nq=n(1−p)=3<5$, so it can not be approximated by a normal distribution.