Final answer:
To find P(X≤19) for the binomial distribution with n=20 and p=0.9, use the binomial cumulative distribution function with parameters (20, 0.9, 19), often accessed through the binomcdf function in statistical calculators or software.
Step-by-step explanation:
You've asked to find the probability P(X≤19) for the binomial random variable X with parameters n=20 and p=0.9. To calculate this, we can use the binomial cumulative distribution function (CDF) because the probability of success (p) is quite high and the number of trials (n) is sufficient for the binomial distribution to be appropriate.
Since we're interested in P(X≤19), we actually want to find the sum of probabilities from X=0 to X=19. Instead of calculating the probabilities for each value of X and summing them up, we can use the function binomcdf available on most statistical calculators or software.
The formula for the CDF of a binomial distribution in this case would be: binomcdf(20, 0.9, 19), which will give us the probability of X being less than or equal to 19. This is exactly what we need to calculate the value of P(X≤19).