Respuesta :
Answer:
For this case we want this probability:
[tex] P( 75 <X< 87) [/tex]
And we can use the z score formula given by:
[tex] z = \frac{87-81}{3} = 2[/tex]
[tex] z = \frac{75-81}{3} = -2[/tex]
So we want the probability for the values within two deviations from the mean and from the empirical rule we know that we have approximately 0.95 or 95% of the values within two deviations from the true mean.
And since we have a total of 120 students we expect:
120*0.95 = 114 between 75g and 87 g
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 σ) of the mean (denoted by µ)".
Let X the random variable who represent the courtship time (minutes).
From the problem we have the mean and the standard deviation for the random variable X. [tex]E(X)=81, Sd(X)=3[/tex]
So we can assume [tex]\mu=81 , \sigma=3[/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:
• The probability of obtain values within one deviation from the mean is 0.68
• The probability of obtain values within two deviation's from the mean is 0.95
• The probability of obtain values within three deviation's from the mean is 0.997
Solution to the problem
For this case we want this probability:
[tex] P( 75 <X< 87) [/tex]
And we can use the z score formula given by:
[tex] z = \frac{87-81}{3} = 2[/tex]
[tex] z = \frac{75-81}{3} = -2[/tex]
So we want the probability for the values within two deviations from the mean and from the empirical rule we know that we have approximately 0.95 or 95% of the values within two deviations from the true mean.
And since we have a total of 120 students we expect:
120*0.95 = 114 between 75g and 87 g
