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:**0.221The 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:**0.996To 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:**0.120To 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:**0.001To 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:**0.634Here, 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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