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. Example 7.12Suppose in a local Kindergarten through 12th grade (K - 12) school district, 53 percent of the population favor acharter 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 standarddeviation are µ = np and ơ =ynpq. The mean is 159 and the standard deviation is 8.6447. The random variablefor the normal distribution is Y. Y ~ N(159, 8.6447). See The Normal Distribution for help with calculatorinstructions.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) = 0.5689For 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) = 0.0741For part e,P(X = 175) has normal approximation P(174.5 < Y< 175.5) = 0.0083.

Name: Suppose in a local Kindergarten through 12th grade (K - 12) school dis
Uploaded: 2024-03-20T07:06:27.000Z
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Description: 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. Example 7.12Suppose in a local Kindergarten through 12