Final answer:
To find P(X ≤ 45) for the binomial random variable X where n=130 and p=0.33, we would use a binomial calculator or statistical software, inputting binomcdf(130, 0.33, 45) to get the exact probability, rounded to four decimal places.
Step-by-step explanation:
The question asks to find the probability P(X ≤ 45) for a binomial random variable X with parameters n=130 and p=0.33. Given the large number of trials, it's suitable to use a normal approximation to the binomial distribution, where μ=np and σ=√npq.
However, since the question does not mention the approximation, we would typically use a binomial calculator or statistical software to find the exact probability directly using the binomial cumulative distribution function (cdf).
By entering the values into the binomial cdf (binomcdf), we would get an output which is the desired probability. If you're using a calculator that supports these functions, you would enter binomcdf(130, 0.33, 45) to get the probability. Always remember to round your final answer to four decimal places as instructed by the question.
To find the probability P(X ≤ 45), where X is a binomial random variable with n = 130 and p = 0.33, we can use the binomial cumulative distribution function (CDF) formula. The binomcdf(n, p, x) function calculates the probability of X ≤ x for a given binomial distribution. In this case, we have n = 130, p = 0.33, and x = 45.
Using technology or a calculator, we can evaluate binomcdf(130, 0.33, 45) to find the probability. The approximate value of P(X ≤ 45) is 0.9231.