What are the R commands used and their outcomes Problem 6 Pe

What are the R commands used and their outcomes?

Problem 6:
Penn State Fleet which operates and manages car rentals for Penn State employees found that the tire lifetime for their vehicles has a mean of 50,000 miles and standard deviation of 3500 miles. They consider a random sample of 50 vehicles. Find the following:

what is the approximate distribution, the mean, and the variance of the mean lifetime? (Hint: Use the CLT)

find the probability that the sample mean lifetime for these 50 vehicles exceeds 52,000

Solution

Mean ( u ) =50000
Standard Deviation ( sd )=3500/ Sqrt ( 50 ) = 494.975
Number ( n ) = 50
Normal Distribution = Z= X- u / (sd/Sqrt(n) ~ N(0,1)                  
P(X > 52000) = (52000-50000)/3500/ Sqrt ( 50 )
= 2000/494.975= 4.0406
= P ( Z >4.0406) From Standard Normal Table
= 0