Use normal approximation to find the probability of the indicated number of voters. In this case, assume that 184 eligible voters aged 18-24 are randomly selected. Suppose a previous study showed that among eligible voters aged 18-24, 22% of them voted.
Probability that fewer than 44 voted.
I am having a hard time figuring out the formula to even attempt this problem. I could use a few good tips to solving this problem.
dadafawefs
To solve this problem using the normal approximation, we can use the following formula:
P(X < x) = P(Z < (x - np) / sqrt(npq))
where:
P(X < x) is the probability that fewer than x voters voted
P(Z < z) is the cumulative probability of the standard normal distribution up to z
x is the number of voters we want to find the probability for (in this case, 44)
n is the number of trials or observations (in this case, 184)
p is the probability of success for each trial (in this case, 0.22 since 22% voted)
q is the probability of failure for each trial (q = 1 - p)
Let's plug in the values and solve:
x = 44
n = 184
p = 0.22
q = 1 - 0.22 = 0.78
First, find the expected number of voters by multiplying the number of trials (n) by the probability of success (p):
np = 184 * 0.22 = 40.48
Next, find the standard deviation by taking the square root of the product of n, p, and q:
sqrt(npq) = sqrt(184 * 0.22 * 0.78) ≈ 5.08
Now, we can calculate the z-value:
z = (x - np) / sqrt(npq) = (44 - 40.48) / 5.08 ≈ 0.6929
Finally, we can find the probability by looking up the z-value in the standard normal distribution table or using a calculator:
P(Z < 0.6929) ≈ 0.7554
Therefore, the probability that fewer than 44 voters aged 18-24 voted is approximately 0.7554.