A binomial experiment consists of 9 independent trials. The probability of success in each is 0.4. Using tables find p(x less than or equal to 3) Set up like this? X. 1 2 3 4 5 6 7 8 9. P(x=x) .4 .4 .4 .4 .4 .4 .4 .4 .4
Its supposed to be a distribution table but it's sloppy since I'm writing from my phone.
Then it asks for the mean and standard deviation. The mean is 18 and SD is 25 right?
To find the probability of getting less than or equal to 3 successes (x ≤ 3) in a binomial experiment with 9 independent trials and a probability of success of 0.4, you can use binomial probability tables.
1. Before using the tables, determine the probability for each value of x (number of successes) from 0 to 3. Since the probability of success in each trial is 0.4, the probability of failure (or "not success") is 1 - 0.4 = 0.6.
- P(x = 0) = (0.6)^9 (probability of 0 successes)
- P(x = 1) = (0.4)^1 * (0.6)^8 (probability of 1 success)
- P(x = 2) = (0.4)^2 * (0.6)^7 (probability of 2 successes)
- P(x = 3) = (0.4)^3 * (0.6)^6 (probability of 3 successes)
2. Now, you can use binomial probability tables to find the cumulative probability of x ≤ 3, which is the sum of the probabilities for x = 0, 1, 2, and 3.
- P(x ≤ 3) = P(x = 0) + P(x = 1) + P(x = 2) + P(x = 3)
You can consult binomial probability tables or use statistical software or calculators capable of calculating binomial probabilities to find the exact values for each probability.