Q4. Tesla Suppose that the distance that a new Tesla can drive on a fully charged...
Q4. Tesla
Suppose that the distance that a new Tesla can drive on a fully charged battery has a mean of 300 miles with a standard deviation of 15 miles. The performance of all Tesla vehicles is similar and independent of each other (We call it i.i.d: independent and identical distribution).
- What is the mean and standard deviation of the average driving distance on a fully charged battery in a sample of 30 cars? ( 2 points)
- What is the mean and standard deviation of the average driving distance on a fully charged battery in a sample of 200 cars? (2 points)
- What is the probability that the mean of driving distance on a fully charged battery is more than 310 miles in a sample of 30 cars? ( 4 points)
- What assumptions did you make to proceed with calculations? (2 points)
Homework Answers
a)
mean = 300 and sd(Xbar) =sd(X) /sqrt(n) = 15/sqrt(30) = 2.7386
b)
mean = 300 and sd(Xbar) =sd(X) /sqrt(n) = 15/sqrt(200) = 1.06066
c)
P(Xbar > 310)
= P(Z > (310 - 300)/2.7386)
= P(Z > 3.6515 )
= 0.0001
d)
iid assumption
random sample
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