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Use the following data. It has been previously established that for a certain type of AA battery (when newly produced), the voltages are distributed normally with $\mu=1.50 \mathrm{V}$ and $\sigma=0.05 \mathrm{V}$.

What percent of the batteries have voltages above $1.64 \mathrm{V} ?$

Intro Stats / AP Statistics

Chapter 22

Introduction to Statistics

Section 4

Normal Distributions

Descriptive Statistics

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03:57

(II) Suppose two batteries…

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(II) Determine the magnitu…

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In Fig. $27-26,$ the ideal…

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In Fig. $25.28,$ take all …

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Consider the circuit shown…

09:26

In Fig. $27-41, R_{1}=10.0…

01:04

A variable DC battery is c…

Welcome to you Marie in the current problem we are considering the distribution of voltages of double A batteries and this voltages are distributed normally. That mean 1.50 votes and sigma 0.5 holes. Now, if we draw the normal distribution over here, that will look something like this. Okay, but this is the mean. Okay, this is the point of symmetry. Uh consider my beautiful drawing here and this is one sigma limit. This is two sigma limit and this is three sigma limit. Now the question that we are asked is what percentage of the uh written Batteries will have voltages above? 1.64, correct. So now 1.64 is again a non standard value. It's not one sigma tau sigma three sigma limit value. So we take the process of standardization x minus mu pi sigma greater than 1.64 minus New. New is 1.50 divided by 0.05, correct. Which is equal to the probability said greater than 0.14 divided by zero 05 Date it is probability zed greater than 14 x five. So this will be said greater than 2.8. Now, what is the value of 2.8 from the tables? So if I bring the table in this will be always um so this will be always 2.8 over here, which is 0.9974. So below, if if we look at the diagram now, So we want to .8 which is 1.64. So 1.64 is going to be somewhere forward. Fear. If you consider it's under stable, the probability of Now this stable gives probability zed less than 2.8 which is 0.9974 But we want greater than so, it will be one minus probability zero less than 2.8. That is one minus zero point 9974 Which is equal to six and then two. And then you know that you know They do 0.0026. But uh probability if we can get that 2%, it it will be 0.26% by multiplying this 100 right? There's little .26% of the entire population. As as you can see like if you ask yourself why why is this list? Because to pointed if you see 1.64 is the value at 1.65 you get the three signal a bit. So just really a very rare value. So something more than that rare value. We have really negligible probability. That is a very negligible percent of the population will go and sit there. So only this percentage will go and sit in this area and

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