Now, all we need to do is read the probability value where the \(p = 0.30\) column and the (\(n = 10, y = 6\)) row intersect.The standard normal distribution is a normal distribution with a mean of zero and standard deviation of 1. Find the 6 in the second column on the left, since we want to find \(F(6)=P(Y\le 6)\).Find \(n=10\) in the first column on the left.Now it's just a matter of looking up the probability in the right place on our cumulative binomial table.
The good news is that we can rewrite \(P(X\ge 4)\)as a probability statement in terms of \(Y\): We can't use the cumulative binomial tables, because they only go up to \(p=0.50\). We are interested in finding \(P(X\ge 4)\). And, if we let \(Y\) denote the number of subscribers who don't qualify for favorable rates, then \(Y\), which equals \(10-X\), is a binomial random variable with \(n=10\) and \(q=1-p=0.30\). If we let \(X\) denote the number of subscribers who qualify for favorable rates, then X is a binomial random variable with \(n=10\) and \(p=0.70\). Shall we make this more concrete by looking at a specific example? Just change the definition of a success into a failure, and vice versa! That is, finding the probability of at most 3 successes is equivalent to 7 or more failures with the probability of a failure being 0.40. What happens if your \(p\) equals 0.60 or 0.70? All you need to do in that case is turn the problem on its head! For example, suppose you have \(n=10\) and \(p=0.60\), and you are looking for the probability of at most 3 successes. Oops! Have you noticed that \(p\), the probability of success, in the binomial table in the back of the book only goes up to 0.50. of the kinds of binomial probabilities that you might need to find. at most \(x\), more than \(x\), exactly \(x\), at least \(x\), and fewer than \(x\). We have now taken a look at an example involving all of the possible scenarios. That is, the probability that fewer than 5 people in a random sample of 15 would have no health insurance is 0.8358. The cumulative binomial probability table tells us that \(P(X\le 4)= 0.8358\). What is the probability that fewer than 5 have no health insurance? That is, the probability that at least one person in a random sample of 15 would have no health insurance is 0.9648. The cumulative binomial probability table tells us that \(P(X\le 0)=0.0352\). What is the probability that at least 1 has no health insurance? Again, for kicks, since it wouldn't take a lot of work in this case, you might want to verify that you'd get the same answer using the binomial p.m.f. That is, there is about a 25% chance that exactly 3 people in a random sample of 15 would have no health insurance. The cumulative binomial probability table tells us that finding \(P(X\le 3)=0.6482\) and \(P(X\le 2)=0.3980\). What is the probability that exactly 3 have no health insurance? That is, the probability that more than 7 in a random sample of 15 would have no health insurance is 0.0042. The cumulative binomial probability table tells us that \(P(X\le 7)=0.9958\). What is the probability that more than 7 have no health insurance? For kicks, since it wouldn't take a lot of work in this case, you might want to verify that you'd get the same answer using the binomial p.m.f. We've used the cumulative binomial probability table to determine that the probability that at most 1 of the 15 sampled has no health insurance is 0.1671.
Let's just take a look at the top of the first page of the table in order to get a feel for how the table works: If you take a look at the table, you'll see that it goes on for five pages.
Standard normal table 0.9444 software#
Now the standard procedure is to report probabilities for a particular distribution as cumulative probabilities, whether in statistical software such as Minitab, a TI-80-something calculator, or in a table like Table II in the back of your textbook. You'll first want to note that the probability mass function, \(f(x)\), of a discrete random variable \(X\) is distinguished from the cumulative probability distribution, \(F(x)\), of a discrete random variable \(X\) by the use of a lowercase \(f\) and an uppercase \(F\). For a discrete random variable \(X\), the cumulative probability distribution \(F(x)\) is determined by: Is called a cumulative probability distribution.