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olasank [31]
3 years ago
15

The lifetime of a certain type of battery is normally distributed with mean value 12 hours and standard deviation 1 hour. there

are nine batteries in a package. what lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages? (round your answer to two decimal places.)
Mathematics
1 answer:
Montano1993 [528]3 years ago
6 0
The probability that a normally distributed dataset with a mean, μ, and statndard deviation, σ, exceeds a value x, is given by

P(X\ \textgreater \ x)=1-P(X\ \textless \ x)=1-P\left(z\ \textless \  \frac{x-\mu}{\frac{\sigma}{\sqrt{n}}} \right)

Given that t<span>he lifetime of a certain type of battery is normally distributed with mean value 12 hours and standard deviation 1 hour and that the probability that </span><span>nine batteries in a package exceeds a certain value, x, is </span>5% or 0.05. Then the value x is given by

P(X\ \textgreater \ x)=0.05 \\  \\ \Rightarrow1-P\left(z\ \textless \ \frac{x-12}{\frac{1}{\sqrt{9}}} \right)=0.05 \\  \\ \Rightarrow P\left(z\ \textless \ \frac{x-12}{\frac{1}{3}} \right)=1-0.05=0.95 \\  \\ \Rightarrow P(z\ \textless \ 3(x-12))=P(z\ \textless \ 1.645) \\  \\ \Rightarrow3(x-12)=1.645 \\  \\ \Rightarrow x-12= \frac{1.645}{3} =0.5483 \\  \\ \Rightarrow x=0.5483+12\approx12.55
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marysya [2.9K]

Answer:

\huge x >  \frac{7}{3}  \\

Step-by-step explanation:

8( \frac{1}{2} x -  \frac{1}{4} ) > 12 - 2x \\

<u>Expand the terms in the bracket</u>

That's

8( \frac{1}{2} x) - 8( \frac{1}{4} ) > 12 - 2x \\ 4x - 2 > 12 - 2x

Move -2x to the other side of the inequality

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<u>Move - 2 to the other side of the inequality</u>

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Divide both sides by 6

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5 0
3 years ago
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6 0
3 years ago
if i measure a hypotenuse and i get 11 and then i double check my work by doing the a squared + b squared = c squared method and
RoseWind [281]
Hi there!

Sometimes, like you said, you might don't get the exact answer when you justified your answer. In this case, you need to take the nearest number. So if you got 11 then 12 is the nearest number, just go for it.

Or go back and start over and see if you didn't miss anything.


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5 0
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Pre image ABCD was dilated to be image A’B’C’D, where the center of dilation is the origin. What scale factor was used in the di
ArbitrLikvidat [17]

Answer:

The scale factor is 0.25

Step-by-step explanation:

we know that

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substitute the values

z=\frac{1'}{4}=0.25

8 0
3 years ago
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