No software required. Vehicle speeds at a certain highway location are approxima
ID: 3126835 • Letter: N
Question
No software required. Vehicle speeds at a certain highway location are approximately normally distributed with a mean of p = 65 mph and standard deviation of a = 5 mph. For each of the following questions, fill in the blank with the appropriate speeds. Apply the Empirical Rule where appropriate./One vehicle is randomly selected; there is about a 68 percentage chance that the vehicle's speed will be between and. One vehicle is randomly selected; there is about a 95% chance that the vehicle's speed will be between and. The speeds of randomly selected samples of 25 vehicles will be recorded. For samples of n = 25 vehicles, there is about a 68 percentage chance that the mean speed of the sample will be between and. The speeds of randomly selected samples of 100 vehicles will be recorded. For samples of n = 100 vehicles, there is about a 99.7 percentage chance that the mean speed of the sample will be between and .Explanation / Answer
Given that the mean (u) of a normal probability distribution is 65 and the
standard deviation (sd) is 5.
(a) About 68% of the area under the normal curve is within one standard deviation of the mean. i.e.
(u ± 1s.d)
So to the given normal distribution about 68% of the observations lie in between
= (65 ± 5)
= [65-5, 65+5]
= [ 60,70 ]
(b)
About 95% of the area under the normal curve is within two standard deviations of the mean. i.e.
(u ± 2*s.d)
So to the given normal distribution about 68% of the observations lie in between
=[65 ± 2 * 5]
= [ 55, 75]
(c) For n=25 , s.d = 5/Sqrt(25) = 1
Practically 99.7% of the area under the normal curve is within three standard deviations of the mean. i.e.
= (65 ± 1)
= [65-1, 65+1]
= [ 64,66 ]
d.
Practically 99.7% of the area under the normal curve is within three standard deviations of the mean. i.e.
(u ± 3*s.d)
For n = 100, s.d = 5/Sqrt(100) = 0.5
=(65 ± 3*(0.5))
=(63.5, 66.5)
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.