### Problem 10 assign 4 RStudio **pleaser type answer**

The lifetime of the timing belt of a certain make of cars is normally distributed with mean 125,000 miles and standard deviation 10,000 miles.

a) Find the probability that a timing belt last until the car runs 140,000 miles. ```{r} #include solution in R

# pnorm() function to calculate probablity # z-score to calculate the probablity #z-score = (x-)/ #x is given as 140000 tm_mean <- 125000; tm_sd <- 10000; x <- 140000; z <- (x-tm_mean)/tm_sd #z = 1.5 pnorm(z,lower.tail = FALSE); #0.0668072 is the probablity that timing belt last 140,000 miles.

``` b) The automaker recommends that owners have the timing belt replaced when the mileage reaches 90,000 miles. What is the probability that the timing belt fails before the car reaches the manufacturer's recommended mileage? ```{r} #include solution in R ``` c) An owner of this type of car wants to take a chance and replace the timing belt at the 1st percentile of the distribution. What should be the mileage of the car when he has the timing belt replaced? ```{r} #include solution in R ```