The life expectancy of a certain tire is a normal distribution with the mean = 40,000 miles, standard deviation is 1,000 miles. find the probability that a tire will last more than 39,000 miles.

Step-by-step explanation:

The average is:

The standard deviation is:

We want the probability that a tire lasts more than 39,000 miles.

This is:

Now we must transform these values to those of a standard normal distribution to facilitate calculation by using the probability tables.

This is:

---------- (For the symmetry of the standard normal distribution)

When you search for the normal standard table, you get the following value:

(x3 + 6x2 + 2x - 6) • (x - 1)

step-by-step explanation:

polynomial long division :

3.2     polynomial long division

dividing :   x4+5x3-4x2-8x+6

                              ("dividend")

by         :     x-1     ("divisor")

dividend     x4   +   5x3   -   4x2   -   8x   +   6

- divisor   * x3     x4   -   x3            

remainder         6x3   -   4x2   -   8x   +   6

- divisor   * 6x2         6x3   -   6x2        

remainder             2x2   -   8x   +   6

- divisor   * 2x1             2x2   -   2x    

remainder               -   6x   +   6

- divisor   * -6x0               -   6x   +   6

remainder                     0

quotient :   x3+6x2+2x-6   remainder:   0

597

step-by-step explanation: