Question

If x is a binomial random variable, use the binomial probability table to find the probabilities below. a. P(x<9) for n=20,p=0.6 b. P(x≥11) for n=15,p=0.8 c. P(x=2) for n=25,p=0.2 Click here to view a portion of the binomial probability table for n=15. Click here to view a portion of the binomial probability table for n=20. Click here to view a portion of the binomial probability table for n=25.

Answer 1

To find probabilities for a binomial random variable using a binomial probability table, one would look up or sum probabilities for the given value(s) of X according to the parameters n and p provided for each scenario.

Step-by-step explanation:

The question involves using the binomial probability table to find specific probabilities for a binomial random variable X with different parameters. We're given three scenarios and asked to find:

P(x < 9) when n=20 and p=0.6,

P(x ≥ 11) when n=15 and p=0.8,

P(x=2) when n=25 and p=0.2.

To find these probabilities:

For P(x < 9), you sum up the probabilities from x=0 to x=8 using a binomial probability table for n=20 and p=0.6.

For P(x ≥ 11), you need to calculate 1 - P(x < 11), which involves summing up the probabilities from x=0 to x=10 and subtracting from 1, using the table for n=15 and p=0.8.

To find P(x=2) for n=25 and p=0.2, directly look up the probability for x=2 in the corresponding table.

When using these tables, it is important to follow the binomial distribution rules and notations such as X ~ B(n, p), μ = np, and the standard deviation σ = √(npq). If the tables are not provided, one may need to use a binomial probability formula or statistical software to perform these calculations.