50.6k views
3 votes
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.

1 Answer

2 votes

Final answer:

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.

User Narayan Yerrabachu
by
8.3k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.