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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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Tresset [83]
I hope this helps you

3 0
3 years ago
an amusement park charge 35.50 for admission.on saturday,6,789 people visited the park.about how much money did the park earn fr
sp2606 [1]
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3 0
3 years ago
Read 2 more answers
The difference between an observational study and an experiment is that:
yulyashka [42]

Answer:

B

Step-by-step explanation:

An experiment is a study carried out in a controlled environment where the person undertaking the research hopes to understand cause and effect between the independent and dependent variables. An example of a experiment is the palovian experiment

The independent variable is the variable that the person carrying out an experiment changes or manipulates. the independent variable usually have a direct effect on the dependent variable

The dependent variable is the variable that is being measured in an experiment. It is usually affected by the independent variable

Observational study is the study where the researcher observes and measures cause and effect between independent and dependent variables without trying  to control or influence the population

4 0
3 years ago
WILL GIVE BRAINLIEST, THANKS, AND 5 STARS!<br> PLEASE HELP ME!
Bogdan [553]

Answer:

-4 and 4

Step-by-step explanation:

<u>Method 1</u>

Apply Difference of Two Squares Formula: a^2-b^2=(a+b)(a-b)

Given  x^2-16=0

Rewrite 16 as 4²

Therefore, a^2=x^2 and b^2=4^2

\implies a = \sqrt{x^2}=x

\implies b=\sqrt{4^2} =4

\implies x^2-16^2=(x+4)(x-4)

\implies (x+4)(x-4)=0

\implies (x+4)=0 \implies x=-4

\implies (x-4)=0 \implies x=4

<u>Method 2</u>

Given equation:

x^2-16=0

Add 16 to both sides:

\implies x^2-16+16=0 + 16

\implies x^2=16

Square root both sides:

\implies \sqrt{x^2}=\sqrt{16}

\implies x=\pm4

Therefore, x = -4, x = 4

6 0
2 years ago
Grace started her own landscaping business. She charges $6 an hour for mowing lawns and $11 per hour for pulling weeds. In Septe
valkas [14]

Answer:

$477

Step-by-step explanation:

63 hours x $6 = $378

9 hours x $11 = $99

378+99= $477

3 0
3 years ago
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