In 14-17 , use the normal approximation to estimate each probability. Round your answers to thre

In 14-17 , use the normal approximation to estimate each...

Key Concepts

Standardization

Standardization is the process of converting a value from a normal distribution into a z-score by subtracting the mean and dividing by the standard deviation. This transformation allows the use of standard normal distribution tables to find probabilities for the original variable under consideration.

Continuity Correction

Continuity correction is a technique applied when a discrete distribution is approximated by a continuous distribution. It involves adjusting the value of the discrete variable by 0.5 to account for the difference between the discrete and continuous nature of the distributions. This correction improves the accuracy of the approximation.

Binomial Distribution

The binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success. It is characterized by two parameters, n (number of trials) and p (probability of success), and is used to calculate probabilities of obtaining a certain number of successes out of these trials.

Normal Approximation to the Binomial

The normal approximation is used when the number of trials, n, is large enough such that the binomial distribution can be approximated by a normal distribution. This approach simplifies calculations by using the properties of the continuous normal distribution to estimate probabilities that would otherwise be computed using the binomial formula.

Transcript

00:01 This is going to be a normal cdf calculator function question, meaning if you don't have a calculator with a normal cdf function, then you will need to go online and search for online calculator with normal cdf function or something like that to find one, but you will need that at the end of this.

00:20 We won't be using it immediately here, but our end result is going to be plugging our low, our high, our mean, and our standard deviation all in.

00:30 To this calculator to figure out what our final answer is.

00:34 Make sure you have that before you continue on with this video.

00:39 Now, assuming that you have that, we do have these four things here in front of us that we need to find, which is the low, the high, the mean, and the standard deviation.

00:47 Now, the low and the high, we should be able to figure out right now just based off what we're being asked to find the probability of.

00:53 In this case, it's asking us to find the probability of fewer than 60 successes, all right meaning 59 or lower right that's what it's saying it's not saying 60 or lower than that it said specifically fewer than 60 so that means 59 is the most amount of successes that we can have and then anything lower than that is also acceptable so that would mean 59 actually represents our high right this time we're going for fewer than 60 so that would represent our high our low would be what's the least amount of successes we can have? well, this is probability we're dealing with some sort of real scenario.

01:33 The lowest we can have is zero.

01:35 You can't do negatives.

01:37 Either you've done no trials at all or you've done at least one trial.

01:40 There's no such thing as negative successes.

01:43 We can just have zero successes.

01:45 So that's our low and our high, between zero and 59.

01:48 That part's pretty straightforward.

01:50 Now we have to find our mean and our standard deviation.

01:53 That's actually going to require some work on our part...