Question
A company knows that the monthly average of licenses submitted during a year by its workers is 6.6, with a deviation of 1.4. With this information, the human resources department believes it can make a projection for the year following. Calculate the probability that the number of licenses for the following year is between 10 and 15. * You must associate the resolution of the exercise with a continuous distribution function.
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Answer to a math question A company knows that the monthly average of licenses submitted during a year by its workers is 6.6, with a deviation of 1.4. With this information, the human resources department believes it can make a projection for the year following. Calculate the probability that the number of licenses for the following year is between 10 and 15. * You must associate the resolution of the exercise with a continuous distribution function.
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4.5108 Answers
First, convert \(X\) to the standard normal variable \(Z\) using the formula:
Z = \frac{X - \mu}{\sigma}
For \(X = 10\):
Z = \frac{10 - 6.6}{1.4} \approx 2.43
For \(X = 15\):
Z = \frac{15 - 6.6}{1.4} \approx 6
Now, we need to find the probability for \(Z\) between these values:
P(2.43 \leq Z \leq 6)
Using standard normal distribution tables or a calculator, we find:
P(Z \leq 6) \approx 1
P(Z \geq 2.43) \approx 0.9925
Thus, the probability is:
P(2.43 \leq Z \leq 6) = P(Z \leq 6) - P(Z \geq 2.43)
P(2.43 \leq Z \leq 6) = 1 - 0.9925 = 0.0075
Therefore, the probability that the number of licenses for the following year is between 10 and 15 is:
\boxed{0.0075}
For \(X = 10\):
For \(X = 15\):
Now, we need to find the probability for \(Z\) between these values:
Using standard normal distribution tables or a calculator, we find:
Thus, the probability is:
Therefore, the probability that the number of licenses for the following year is between 10 and 15 is:
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