12 of 35 shirts are old. What percentage of the shirts are old?
2 answers:
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Answer:
b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941
Step-by-step explanation:
An uniform probability is a case of probability in which each outcome is equally as likely.
For this situation, we have a lower limit of the distribution that we call a and an upper limit that we call b.
The mean of the uniform probability distribution is:
The standard deviation of the uniform distribution is:
The probability that we find a value X lower than x is given by the following formula.
Uniform distribution between 2.93 and 3.1 volts
This means that . So
Mean:
Standard deviation:
What is the probability that a battery has a voltage less than 2.98?
So the correct answer is:
b. E(X) = 3.015, STDEV(X)= 0.049, P (X ≤ 2.98) = 0.2941
Answer:
a)
b)
Step-by-step explanation:
1) Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
2) Part a
Let X the random variable that represent the duration of a safe dosage of pain relief drug, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way:
And in order to find these probabilities we can find tables for the normal standard distribution, excel or a calculator.
3) Part b
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
And we can find this probability on this way: