Respuesta :
Answer:
[tex]\mu -3\sigma = 76 -3*2.5 = 68.5[/tex]
[tex]\mu +3\sigma = 76 +3*2.5 = 83.5[/tex]
So then we expect the 99.7% of the finishing times would be between 68.5 s and 83.5 s for the 400 meters race
Step-by-step explanation:
Let X the random variable who represent the finishing times.
From the problem we have the mean and the standard deviation for the random variable X. [tex]E(X)=76, Sd(X)=2.5[/tex]
So then the parameters are [tex]\mu=76,\sigma=2.5[/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 , within two deviations we have 0.95 and within 3 deviations from the mean is 0.997
And from this rule we have 99.7 % of the values within 3 deviations from the mean, so we can find the limits like this:
[tex]\mu -3\sigma = 76 -3*2.5 = 68.5[/tex]
[tex]\mu +3\sigma = 76 +3*2.5 = 83.5[/tex]
So then we expect the 99.7% of the finishing times would be between 68.5 s and 83.5 s for the 400 meters race
