Suppose in a local Kindergarten through 12th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through 5. A simple random sample of 300 is surveyed. 5...

Extracted text: Example 7.12 Suppose in a local Kindergarten through 12th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through 5. A simple random sample of 300 is surveyed. a. Find the probability that at least 150 favor a charter school. b. Find the probability that at most 160 favor a charter school. c. Find the probability that more than 155 favor a charter school. d. Find the probability that fewer than 147 favor a charter school. e. Find the probability that exactly 175 favor a charter school. Let X = the number that favor a charter school for grades K trough 5. X ~ B(n, p) where n = 300 and p = 0.53. Since np > 5 and nq > 5, use the normal approximation to the binomial. The formulas for the mean and standard deviation are µ = np and ơ = ynpq. The mean is 159 and the standard deviation is 8.6447. The random variable for the normal distribution is Y. Y ~ N(159, 8.6447). See The Normal Distribution for help with calculator instructions. For part a, you include 150 so P(X > 150) has normal approximation P(Y > 149.5) = 0.8641. normalcdf(149.5,10^99,159,8.6447) = 0.8641. For part b, you include 160 so P(X < 160)="" has="" normal="" appraximation="" p(y="">< 160.5)="0.5689." normalcdf(0,160.5,159,8.6447)="0.5689" for="" part="" c,="" you="" exclude="" 155="" so="" p(x=""> 155) has normal approximation P(y > 155.5) = 0.6572. normalcdf(155.5,10^99,159,8.6447) = 0.6572. For part d, you exclude 147 so P(X < 147)="" has="" normal="" approximation="" p(y="">< 146.5)="0.0741." normalcdf(0,146.5,159,8.6447)="0.0741" for="" part="" e,p(x="175)" has="" normal="" approximation="" p(174.5=""><>< 175.5) = 0.0083. 175.5)="">