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What is the probability that the sample of kindergarten children in Example 7.6 has a mean height of less than 39.75 inches?

0.970

Intro Stats / AP Statistics

Chapter 7

Sample Variability

Section 3

Application of the Sampling Distribution of Sample Means

Sampling and Data

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okay for this problem? Were you referring back to a previous example about heights of kindergarten Children? So I'm the previous example. We were told that, uh, for this problem, we're told that the population height for these kindergarten kids is 39.0 inches. Okay. And the standard deviation of the population was to and in the example, they looked in between problem, they looked at a the probability the mean value would be between 38.5 and 40. But for this problem, we want to find out is we want to find out What's the probability? I'm just going to restate this using probability rotation way. Want with probability that the height, the X we'll call it random variable is less mean. Height of the Children is less than 39.75 inches. So similar deal. We know that it's a normal distribution problem. We can use these scores and find some information on the table. And we know at the end of the day the sample size makes a difference in terms of our variability in. So let's write that down to sample size was 25. Okay, so first things first you do your Z score? Ah, over here. Plan to the score formula. So we'll do. Um, the 39.75 you plan these two? These were formula here. This minus 39.0. Divided by the standard deviation, which is adjusted for the sample size of 25. So if we do a formula substitute simplify, we get 0.75. I was gonna give you a whole number. There's a 0.75 divided by 2/5. And so that gives us 1.875 in the end. So we're going to say approximately 1.88 so we can read off the table. So that gives us a positive Z score. 1.88 which makes sense to good chunk above the have the mean there in the population. Mean So then over here, I have my table ready to go. So this is similar standardized table of Z sports and values. So I want to look at a Z score of 1.88 so I'm gonna go over here to 1.8 and 1.8 and 1.88 is down here. So 1.88 looks like it's 0.9699 So about 0.970 s. So in the end, we're going to say the probability. It's a 97% probability garrison from the table, it's, ah, 0.970 probability. So figured out our Z score and with the table and the table will tell us the probability.

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