Using the Central Limit Theorem · Exercise 34

Suppose in a local Kindergarten through 12^th grade (K - 12) school district, 53 percent of the population favor a charter school for grades K through five. A simple random sample of 300 is surveyed. Calculate following using the normal approximation to the binomial distribtion.

(a) Find the probability that less than 100 favor a charter school for grades K through 5.
(b) Find the probability that 170 or more favor a charter school for grades K through 5.
(c) Find the probability that no more than 140 favor a charter school for grades K through 5.
(d) Find the probability that there are fewer than 130 that favor a charter school for grades K through 5.
(e) Find the probability that exactly 150 favor a charter school for grades K through 5.
If you have access to an appropriate calculator or computer software, try calculating these probabilities using the technology.

OpenStax, Introductory Statistics 2e · §7.3 Using the Central Limit Theorem · Exercise 34