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atroni [7]
3 years ago
12

The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. There

are four 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?
Mathematics
1 answer:
tankabanditka [31]3 years ago
3 0

Answer:

The lifetime value needed is 11.8225 hours.

Step-by-step explanation:

Problems of normally distributed samples can be solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by

Z = \frac{X - \mu}{\sigma}

After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we This p-value is the probability that the value of the measure is greater than X.

In this problem, we have that:

The lifetime of a certain type of battery is normally distributed with mean value 11 hours and standard deviation 1 hour. This means that \mu = 11, \sigma = 1.

What lifetime value is such that the total lifetime of all batteries in a package exceeds that value for only 5% of all packages?

This is the value of THE MEAN SAMPLE X when Z has a pvalue of 0.95. That is between Z = 1.64 and Z = 1.65. So we use Z = 1.645

Since we need the mean sample, we need to find the standard deviation of the sample, that is:

s = \frac{\sigma}{\sqrt{4}} = 0.5

So:

Z = \frac{X - \mu}{s}

1.645 = \frac{X - 11}{0.5}

X - 11 = 0.5*1.645

X = 11.8225

The lifetime value needed is 11.8225 hours.

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A fair coin is flipped 120 times. Estimate the expected number of ‘heads’.
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7 0
2 years ago
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Write the following quotient scientific notation 33x10 to the ninth power by 11x10 to the seventh power
zepelin [54]

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10

Step-by-step explanation:

i feel that is the right awnser

6 0
2 years ago
Need a little help with one please
Pani-rosa [81]

Answer:

That would be the side-side-side (SSS) postulate, which states that if all the sides of a triangle are in a fixed ratio to all the corresponding sides of another triangle, then the two triangles are said to be congruent.

Step-by-step explanation:

Looking at triangles ABC and DEF, we notice that:

\frac{AB}{DE} = \frac{AC}{DF}=\frac{BC}{EF}

since

\frac{3}{18} = \frac{6}{36}=\frac{7}{42}=\frac{1}{6}

Let me know if you have further questions.

4 0
3 years ago
H(n)=-2n(2)+4; Find h(4)
anygoal [31]

Answer:

h(4) = –12

Step-by-step explanation:

⇒ What the question is asking is that when the function h(n) = –2n(2) + 4 is h(4), what will the function repond to when solving for h(4)? So, solve for the function h(4):

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⇒ Since n was replaced with 4 in the function h(4), substitute any n for 4 into the function:

h(4) = –2(4)(2) + 4

⇒ Simplify:

h(4) = –16 + 4

⇒ Solve:

h(4) = –12

<u>Answer:</u> h(4) = –12

<em>I hope you understand and that this helps with your question! </em>:)

8 0
3 years ago
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