An operation manager at an electronics company wants to test their amplifiers. The design engineer claims they have a mean outpu
1 answer:
Answer:
The probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers is 0.8078.
Step-by-step explanation:
According to the Central Limit Theorem if an unknown population is selected with mean μ and standard deviation σ and appropriately huge random samples (n > 30) are selected from this population with replacement, then the distribution of the sample means will be approximately normally.
Then, the mean of the sample means is given by,
And the standard deviation of the sample means is given by,
The information provided is as follows:
Compute the probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers as follows:
*Use a <em>z</em>-table.
Thus, the probability that the mean amplifier output would be greater than 449.8 watts in a sample of 76 amplifiers is 0.8078.
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Answer:
a) For this case we can find the cumulative distribution function first:
So then by the complement rule we have this:
b)
So then we have this using independence:
We want to find the following probability:
Using the definition of conditional probability we got:
And we see that if a = 2 and b=5 we have:
c) For this case we use independent identical and with the same distribution experiments.
And the result for part b makes sense since we are interest in find the probability that the random variable of interest would be higher than an specified value given another condition with a value lower or equal.
Step-by-step explanation:
Previous concepts
The geometric distribution represents "the number of failures before you get a success in a series of Bernoulli trials. This discrete probability distribution is represented by the probability density function:"
If we define the random of variable Y we know that:
Part a
For this case we can find the cumulative distribution function first:
So then by the complement rule we have this:
Part b
For this case we can use the result from part a to conclude that:
So then we have this assuming independence:
We want to find the following probability:
Using the definition of conditional probability we got:
And we see that if a = 2 and b=5 we have:
Part c
For this case we use independent identical and with the same distribution experiments.
And the result for part b makes sense since we are interest in find the probability that the random variable of interest would be higher than an specified value given another condition with a value lower or equal.
mutiply the sides together to get a value and subtract the inside area of the frame to find the area.
Frame
Area inside
16*20 = 320