Question

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).

1. 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)
2. 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)
3. 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)
4. What assumptions did you make to proceed with calculations? (2 points)

Answer 1

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