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A recent study of the lifetimes of cell phones found the average is 24.3 months. The standard deviation is 2.6 months. If a company provides its 33 employees with a cell phone, find the probability that the mean lifetime of these phones will be less than 23.8 months. Assume cell phone life is a normally distributed variable.

.1357

Intro Stats / AP Statistics

Chapter 6

The Normal Distribution

Section 3

The Central Limit Theorem

Probability Topics

Temple University

Piedmont College

University of St. Thomas

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Based on this problem, we know that a cell phone has a lifetime average of being 24.3 months with a standard deviation of 2.6 months. And this is information dealing with the population of cell phones. And in this problem, the company is going to provide 33 employees with the cell phone. So, in essence, we're drawing a sample of cell phones from this population with the 33 cell phones, and the question is asking us what is the probability, or find the probability that they mean, which is the X bar is less than 23.8 months. So because we're talking about a sample of 33 people getting cell phones and we want the distribution of the average of those cell phones were going to apply the central Limit Theorem and the Central Limit Theorem says that the average of the means is the same as the average of the population, which is 24.3, and the standard error of the mean, or the standard deviation of the means is the same as the standard deviation of the population divided by the square root of end. So that's in this case going to be a 2.6 divided by the square root of 33. So we're going to want to draw an image, a bell shaped curve to reflect the problem. And we always put our average in the center and are averages 24.3. And the problem is asking us about being less than 23.8. So we're talking 23.8 right here, and we want to go less than so. The next thing we're gonna need to do is we're going to need to find the Z score associated with 23.8. So the Z score would be 23.8 minus 24.3, divided by standard error of the mean We should be 2.6 over the square root of 33 and the Z score turns out to be approximately negative 1.10 So the 23.8 is negative 1.10 meaning it's 1.10 standard deviations below the mean. So what we can do is we can rewrite this problem instead of talking in terms of the X score we can say that the probability that the averages less than 23.8 is no different than the probability that the Z score is less than negative 1.10 And at that point we would go to the standard normal distribution table in the back of your textbook and the probability that the Z is less than negative 1.10 is 0.13 57 So, to recap, our answer. The question waas that if we give cellphones to 33 people, what is the probability that the average of those 33 cell phone less less than 23.8 months and your answer be 0.1357?

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