Question

suppose that 65% of all registered voters in an area favor a certain policy. Among 225 randomly selected registered voters, find the following:

P(x ≤ 150)

, the probability that at most 150 favor the policy? Round to two decimal places.

P(x ≥ 140)

, the probability that at least 140 favor the the policy? Round to two decimal places.

Answer 1

This is like a binomial experiment because there are only 2 possible outcomes :registered voters in an area favor a certain policy or they don't favor. Also each of the result of the voters is independent of each other and there are more than 1 voter.

Let 'X' be the no. of voters who are in favor

The probability of success (in favor ) = 65% = 0.65

n = 225

Since n > 30   and np > 5 (146.25 > 5)

We can approximate this to normal distribution where

=

z-score =

Note: Binomial is a discrete and normal is a continuous distribution so we will need to do a continuity correction since we are approximating discrete to continuous.

=

= P (Z < 0.59)

...........This value can be obtained from normal probability tables,excel function 'normsdist(z)'

=

The probability that at most 150 favor the policy is 0.72

=

= P (Z > -0.94)

= P(Z < 0.94)

=

The probability that at least 140 favor the the policy is 0.83