Final answer:
The probability of x being less than or equal to 2 depends on the type of distribution. For a Poisson distribution with a mean of 1.7292, P(x ≤ 2) is found using the poissoncdf function, resulting in approximately 0.7495. For a binomial distribution, functions like binomcdf are used with the specific parameters to find the cumulative probability.
Step-by-step explanation:
To find the probability of x being less than or equal to 2, we can use the provided information along with the characteristics of the distribution involved. If we're dealing with a binomial distribution, Poisson distribution, or any other specific probability distribution, different methods are applied.
For a Poisson distribution with parameter λ = 1.7292, the probability P(x = 2) is calculated using the poissonpdf function, which yields approximately 0.2653. To find P(x ≤ 2), we can use the poissoncdf function, giving us 1 - P(x > 2) = 1 - 0.2505 = 0.7495.
For a binomial distribution with parameters n and p, you might use the binomcdf function on a calculator as shown in one of the examples, where to find P(x ≤ 12) for n = 20 and p = 0.41, the result is 0.9738.
The general principle is that the area under the probability density function (pdf) for a continuous variable, or the sum of probabilities for a discrete variable, from the minimum value up to x, represents the cumulative distribution function (cdf), which is what P(x ≤ 2) asks for. If the pdf or probability mass function (pmf) is known, you integrate or sum, respectively, over the desired range to find the cumulative probability.