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solmaris [256]
3 years ago
12

An electrical firm manufactures light bulbs that have a length of life that is approximately normally distributed, with mean equ

al to 800 hours and a standard deviation of 40 hours. Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.
Mathematics
1 answer:
kompoz [17]3 years ago
5 0

Answer:

0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

Step-by-step explanation:

The Central Limit Theorem estabilishes that, for a random variable X, with mean \mu and standard deviation \sigma, a large sample size can be approximated to a normal distribution with mean \mu and standard deviation \frac{\sigma}{\sqrt{n}}

Normal probability distribution.

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}

The Z-score measures how many standard deviations the measure is from the mean. 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 get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 800, \sigma = 40, n = 16, s = \frac{40}{\sqrt{16}} = 10

Find the probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

This probability is the pvalue of Z when X = 775. So

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

Z = \frac{775 - 800}{10}

Z = -2.5

Z = -2.5 has a pvalue of 0.0062. So there is a 0.62% probability that a random sample of 16 bulbs will have an average life of less than 775 hours.

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snow_tiger [21]

Answer:

your family

Step-by-step explanation:

1,900/2 = 950

2,700/3 = 900

your family travels 950 miles every day whereas their family travels 900 miles every day :)

6 0
2 years ago
Sam is saving for a guitar. He already has $50 saved and intends to save $30 each week. At week 12, how much money will Sam have
PolarNik [594]

Answer:

$50 + ($30 x 12) = $410

Step-by-step explanation:

8 0
3 years ago
Help po plss
VashaNatasha [74]

Answer:

1. 10:8 = 5:4 (simplest form)

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3 0
3 years ago
For 3/5=2/3t how do you get t=9/10
lesya [120]

Answer:

Step-by-step explanation:

3/5 = 2/3t......multiply both sides by 3/2...this cancels out the 2/3 on the right side

3/5 * 3/2 = t

9/10 = t

another way to do it is this way...

3/5 = 2/3t......divide both sides by 2/3

(3/5) / (2/3) = t

3/5 * 3/2 = t

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7 0
3 years ago
Zena needs an Actor. Actor A charges $250 in addition to $50 per day. Actor B charges $ 200 in addition to $60 per day. When do
Sav [38]

Well I like to start with a base number. Ten. Ten days.

--Without Initial Costs--

Actor A after 10 days -  $500

Actor B after 10 days -  $600

A after 15 days -  $750 + $250 = $1000

B after 15 days -  $900 + $200 = $700

A after 5 days -  $250 + $250 = $500 <|

                                                          /\ \/ -ANSWER

B after 5 days -  $300 + $200 = $500 <|

A after 3 days -  $150 + $250 = $400

B after 3 days -  $180 + $200 = $380

A after 8 days -  $400 + $250 = $650

B after 8 days -  $480 + $200 = $680

Now there, I did a whole bunch of em. Now to add the initial costs. (I did the adding on the same numbers that I just typed so it may be confusing that NOW I am saying to do it when it is already done. LOL)

Basically after all that, the answer is 5 days.

Hope this helps!


5 0
3 years ago
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