Respuesta :
Answer:
For this case we want to find this probability:
[tex] P(10<X<64) [/tex]
And we can use the z score formula to see how many deviation we are within the mean and we got:
[tex] z = \frac{10-37}{9}=-3[/tex]
[tex] z = \frac{64-37}{9}=3[/tex]
And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.
Step-by-step explanation:
Previous concepts
The empirical rule, also known as three-sigma rule or 68-95-99.7 rule, "is a statistical rule which states that for a normal distribution, almost all data falls within three standard deviations (denoted by Ļ) of the mean (denoted by Āµ)".
Let X the random variable who represent the number of phone calls answered.
From the problem we have the mean and the standard deviation for the random variable X. [tex]E(X)=37, Sd(X)=9[/tex]
So we can assume [tex]\mu=37 , \sigma=9[/tex]
On this case in order to check if the random variable X follows a normal distribution we can use the empirical rule that states the following:
ā¢ The probability of obtain values within one deviation from the mean is 0.68
ā¢ The probability of obtain values within two deviation's from the mean is 0.95
ā¢ The probability of obtain values within three deviation's from the mean is 0.997
Solution to the problem
For this case we want to find this probability:
[tex] P(10<X<64) [/tex]
And we can use the z score formula to see how many deviation we are within the mean and we got:
[tex] z = \frac{10-37}{9}=-3[/tex]
[tex] z = \frac{64-37}{9}=3[/tex]
And for this case we know that within 3 deviation from the mean we have 99.7% of the values and that's the answer for this case.
