For the sample questions here, X is a random variable with a binomial distribution with n = 11 and p = 0.4. Use the binomial table to answer the following problems.
Sample questions
What is P(X = 5)?
Answer: 0.221
The binomial table has a series of mini-tables inside of it, one for each selected value of n. To find P(X = 5), where n = 11 and p = 0.4, locate the mini-table for n = 11, find the row for x = 5, and follow across to where it intersects with the column for p = 0.4. This value is 0.221.
What is P(X > 0)?
Answer: 0.996
To find the probability that X is greater than 0, find the probability that X is equal to 0, and then subtract that probability from 1. This makes the calculations much easier.
The binomial table has a series of mini-tables inside of it, one for each selected value of n. To find P(X = 0), where n = 11 and p = 0.4, locate the mini-table for n = 11, find the row for x = 0, and follow across to where it intersects with the column for p = 0.4. This value is 0.004. Now subtract that from 1:
What is
Answer: 0.120
To find the probability that X is less than or equal to 2, you first need to find the probability of each possible value of X less than 2. In other words, you find the values for P(X = 0), P(X = 1), and P(X = 2).
To find each of these probabilities, use the binomial table, which has a series of mini-tables inside of it, one for each selected value of n. To find P(X = 0), where n = 11 and p = 0.4, locate the mini-table for n = 11, find the row for x = 0, and follow across to where it intersects with the column for p = 0.4. This value is 0.004.
Now do the same for the other probabilities: P(X = 1) = 0.027 and P(X = 2) = 0.089. Finally, add these probabilities together:
What is P(X > 9)?
Answer: 0.001
To find the probability that X is greater than 9, first find the probability that X is equal to 10 or 11 (in this case, 11 is the greatest possible value of x because there are only 11 total trials).
To find each of these probabilities, use the binomial table, which has a series of mini-tables inside of it, one for each selected value of n. To find P(X = 10), where n = 11 and p = 0.4, locate the mini-table for n = 11, find the row for x = 10, and follow across to where it intersects with the column for p = 0.4. This value is 0.001.
Now do the same for P(X = 11), which gives you 0.000. (Note: P(X = 11) isn't exactly 0.000 here; it's just a smaller probability than can be expressed in the four decimal places used in this table.) Finally, add the two probabilities together:
What is
Answer: 0.634
Here, you want to find the probability equal to 3 and 5 and everything in between. In other words, you want the probabilities for X = 3, X = 4, and X = 5. You know that n = 11 and p = 0.4, which is the probability of success on each trial.
To find each of these probabilities, use the binomial table, which has a series of mini-tables inside of it, one for each selected value of n. To find P(X = 3), where n = 11 and p = 0.4, locate the mini-table for n = 11, find the row for x = 3, and follow across to where it intersects with the column for p = 0.4. This value is 0.177.
Now do the same for the other probabilities: P(X = 4) = 0.236 and P(X = 5) = 0.221. Finally, add these probabilities together:
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