Question

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 600 is surveyed. Calculate the following using the normal approximation to the binomial distribution. (Round your answers to four decimal places.)

(a) Find the probability that less than 240 favor a charter school for grades K through 5.


(b) Find the probability that 315 or more favor a charter school for grades K through 5.


(c) Find the probability that no more than 290 favor a charter school for grades K through 5.


(d) Find the probability that there are fewer than 280 that favor a charter school for grades K through 5.


(e) Find the probability that exactly 300 favor a charter school for grades K through 5.

Answer 1

Let X denote the number of people who favor a charter school. Then

Using Normal approximation to Binomial distribution,

a)

{Due to continuity correction as a result of using Normal approximation for Binomial distribution}

b)

c)

d)

{Due to continuity correction as a result of using Normal approximation for Binomial distribution}