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Make the given changes in the indicated examples of this section and then solve the indicated problem. In Example $5(\mathrm{b}),$ change 320 to 360 and then find the resulting percentage of batteries.
Intro Stats / AP Statistics
Chapter 22
Introduction to Statistics
Section 4
Normal Distributions
Descriptive Statistics
Temple University
Missouri State University
Idaho State University
Lectures
0:00
06:57
Consider the circuit shown…
03:42
05:03
In the circuit of Figure $…
01:02
See Sample Problem $A$.
17:23
(II) Determine the magnitu…
05:02
(a) Given a 48.0-V battery…
02:41
Two resistors, $A$ and $B$…
01:19
The current through the ba…
00:41
Consider the four types of…
03:20
Determine (a) the equivale…
Welcome to new Madrid. In the current problem we are given that the variable X follows a normal distribution between 400 sigma to be 15 now. Yeah. Just sit the more the lifetimes of batteries, lifetimes off batteries in ours that is this is 400 hours and this is 50 hours. That means what on and average these bulbs will be the lifetime will be 400 hours. And sometimes you know for some uh cases you will see like four 50 it can go and it can also hit 3 50. There is a high chance of that. Okay we can get a value fairly occurring in somebody's real life to be these. And then you can still find like 500 and 300. Somebody can have 305 hours husband. But that chance is a little low and so on. So now the question is probability what is the probability that the batteries life will exceed 3 60? Okay so for that what we can do we can do a standardization but before that I must tell you man, ladies other me the direct interest directly evaluating it. We can use this so that the values are obtained directly. Now this is where I said something but that doesn't make any sense what values are obtained directly or easily. I will explain this feature after two seconds. Now this here if I do standardization it would be x minus meal by sigma. Greater than 3 60 minus new by sigma. Okay now this would be one minus the probability. Now this is Z greater than 3 60 minus 400 by 50. Cut it. So that would be one minus probability said greater than for by 50.8 minus of 0.8 not think of the normal distribution. For a moment it is a value, this is zero, this is negative. Zero pointed correct. So greater than 3 60 would be So if we are thinking from this point of view, we will go So this is nick minus 0.8 right now, I will show you in terms of this. If we had directly done it would have been said greater than zero point Okay, so 0.8 minutes. If this is 0.8 this will be greater than you appointed. Okay, so both this would give us a my area. How that greater than 0.8. Is this area correct? This right, right side shaped like this now, probability zero rather than minus 0.8. Is this okay? This right area and one minus means this area, correct? So this would give that left. Whereas this one gives the right to both are same if you consider by area because normal distribution is symmetric, both are saying. So whatever way we are choosing that way, even from this we can go to the switch back to this. So it is probabilities that greater than zero point it will be one minus probability zero Lisbon zero point eat positive 0.8. And that is nothing. But probability of zet greater than 0.8. But this cannot be obtained from the normal table directly normal table, this value is given so let us be the normal table for your reference. Yeah, report over here. You can see as you know Quiet eat this is the value. Okay that means probability one minus this would be 0.7881 that is nine and then one and then one and then sure 0.2119 So the probability at the battle is would last beyond 3 16 is this? Uh The first thing that would be 21.19 percent. So 21.19% of the total production of batteries, like out of 121.19 batteries, habits have fair chance to are going to have a life lifetime more than 3 60. So I hope you could understand this. Let me know if you have an english.
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