Question

A national survey has shown that approximately 38% of undergraduate students are part-time. If you select 33 undergraduate students, and ask them if they are part-time, find the following. Round all answers to at least 6 decimal places, if needed.

What is the probability that fewer than three students are part-time?

Find the mean, variance, and standard deviation of the binomial distribution.

mean =

variance =

standard deviation =

Answer 1

To find the probability that fewer than three students are part-time, we can use the binomial distribution. The mean, variance, and standard deviation of the binomial distribution can be calculated using the formula.

Step-by-step explanation:

To find the probability that fewer than three students are part-time, we can use the binomial distribution. The probability of success (being part-time) is 0.38, and the number of trials is 33. We want to find the probability of having 0, 1, or 2 successes. Using a binomial calculator or formula, we can add the probabilities of these three outcomes to get the final probability.

The mean of a binomial distribution can be calculated by multiplying the number of trials (33) by the probability of success (0.38), which gives us 12.54. The variance can be calculated by multiplying the mean by the probability of failure (1 - 0.38) and the number of trials, which gives us 7.79. The standard deviation can be found by taking the square root of the variance, which is approximately 2.79.