Question

Let x represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities. (Do not round intermediate calculations. Round your final answers to 4 decimal places.)

Answer 1

This question involves calculating probabilities using a binomial distribution, denoted as X ~ B(n, p), and applying the continuity correction for better approximation of probabilities. This concept is typically covered at the college level in statistics or probability courses.

Step-by-step explanation:

The question asks for the calculation of probabilities using a binomial distribution. If x represents the number of successes, then x follows a binomial distribution with parameters n and p, denoted by X ~ B(n, p). For accurate calculations, especially when the distribution is similar in shape to the normal distribution, it is recommended to use the continuity correction by adding or subtracting 0.5 to the value of x, based on whether we look for 'less than' or 'greater than' probabilities.

In scenarios where the probability of success is low and the number of trials is high, a Poisson distribution can also be used as an approximation to the binomial distribution. However, this approximation is not relevant for the given scenario as p=0.36 does not qualify as a low probability of success.