Final answer:
To find the probability of at least 90 out of 148 registered voters voting in the presidential election, you can use the binomial probability formula. The formula is P(X ≥ k) = 1 - P(X < k), where X is the number of registered voters who will vote, and k is the number we want to find the probability for. You will need to calculate the probabilities for X = 0, 1, 2, ..., 89 and subtract them from 1 to get the probability of at least 90 voters voting.
Step-by-step explanation:
To find the probability that at least 90 out of 148 registered voters will vote in the presidential election, we can use the binomial probability formula. The formula is:
P(X ≥ k) = 1 - P(X < k), where X is the number of registered voters who will vote, and k is the number we want to find the probability for.
In this case, we want to find the probability of at least 90 registered voters voting, so k = 90. The probability that a registered voter will vote in the presidential election is 0.65.
Using the formula, we can calculate:
P(X ≥ 90) = 1 - P(X < 90)
P(X ≥ 90) = 1 - P(X = 0) - P(X = 1) - ... - P(X = 89)
P(X ≥ 90) = 1 - (0.35)(148) - (0.35)(0.65)(148) - (0.35^2)(0.65)(148) - ... - (0.35^89)(0.65)(148)
This calculation can be quite time-consuming, but with the use of technology or a statistical calculator, the probability can be easily obtained.