Respuesta :
Answer:
a) Approximately 34% of braking times are in this interval.
b) 695 ms
Step-by-step explanation:
The Empirical Rule states that, for a normally distributed random variable:
68% of the measures are within 1 standard deviation of the mean.
95% of the measures are within 2 standard deviation of the mean.
99.7% of the measures are within 3 standard deviations of the mean.
In this problem, we have that:
Mean = 535
Standard deviation = 80
A) Approximately what percentage of braking times are in the interval (535, 615)?
The empirical rule is symmetric, which means that 50% of the measures are below the mean and 50% are above.
615 = 535 + 80
So 615 is one standard deviation above the mean.
535 is the mean.
Of the measures above the mean(50%), 68% are within 1 standard deviation of the mean.
Then
0.5*0.68 = 0.34
Approximately 34% of braking times are in this interval.
B) What value do the top 2.5% of braking times exceed?
95% of the measures are within 2 standard deviation of the mean. That is, between the bottom 100 - (95/2) = 2.5% and the top 100 + (95/2) = 2.5% are within 2 standard deviations of the mean.
The top 2.5% are more than two standard deviations of the mean.
535 + 2*80 = 695
So the top 2.5% of braking times exceed 695 ms.
