Binomial Distributions 2 Statistics Lesson 14: Individual Preparation Name: 1. We learned previously how to find probabilities ofa binomial distribution using the probability distribution table and with the IT-83/84 calculator using the binompdf function. In all of those problems, the number of trials, n, was relatively small (less than 20). What would happen if we had a large number of trials, for example n = 40? We could make a really long table and then add up the probabilities that we need. However, this would be rather time consuming. Fortunately, there is another way. We can use binomcdf (binomial cumulative density function) on our calculator. The binomcdf function requires the same parameters as binompdf lie. n, p, and r). However, binomcdf finds the probability of having successes less than or equal to r. P(X s r) = binomcdn, p, r) While you can use binomcdf to find probabilities involving other inequalities {), you do need to rewrite those as follows so that they use only a S inequality: P(X r) = 1 P(X S r) = 1 binomcdf(n,p,r) a. Why do you need to subtract the binomcdf expression from 1 for the 2_> or the > probabilities? 2. A company sells flower and vegetable seeds. For a particular type of seed, the germination rate is 85%. Each packet contains 65 seeds {assume seed distribution is random). To keep customers happy, the manufacturer wants the packets to have 50 or more seeds that germinate. a. From a randomly selected seed packet, find the probability that at least 50 seeds will germinate. i. Which inequality is being used for the probability in this problem? i. Write the binomcdf expression that you will need to use to find this probability. iii. What is the resulting probability? b. Find the probability that less than 50 of the 65 seeds in a packet germinate. c. Find the probability that at most 50 of the 65 seeds in a packet germinate. d. Find the probability that more than 50 of the 65 seeds in a packet germinate. e. Find the probability that exactly 50 of the 65 seeds in a packet germinate