The number of surface flaws in a plastic roll used in the interior of automobiles has a poisson distribution with a mean of 0.07 flaw per square foot of plastic roll. assume an automobile interior contains 10 square feet of plastic roll. round your answers to four decimal places (e. g. 98.7654). (a) what is the probability that there are no surface flaws in an auto interior?

There is a 49.6585% probability that there are no surface flaws in an auto interior

Step-by-step explanation:

In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:

In which

x is the number of sucesses

e = 2.71828 is the Euler number

is the mean in our unit interval.

In this problem

We have mean of 0.07 flaw per square foot of plastic roll. Assume an automobile interior contains 10 square feet of plastic roll. So

(a) What is the probability that there are no surface flaws in an auto interior?

This is

There is a 49.6585% probability that there are no surface flaws in an auto interior

x = central angle apc = measure of minor arc ac

the two angles x and 30 add to 180, so x+30 = 180 and x = 180-30 = 150. the measure of minor arc ac is 150 degrees.

what we need to do from here is find the circumference and then multiply it by x/360 since there are 360 degrees in a circle. in this case, x = 150, so x/360 = 150/360 = 15/36 = 5/12. the shortest distance along the curve from a to c is 5/12 of the distance around the entire circle (aka circumference)

c = circumference

c = pi*d

c = pi*24

c = 24pi

now multiply this by 5/12 to get

distance along minor arc ac = (5/12)*(circumference)

distance along minor arc ac = (5/12)*(24pi)

distance along minor arc ac = 10pi

the formula you can use is

l = (x/360)*pi*d

with

l = length of minor arc

x = central angle

d = diameter

which essentially is the steps we took though a bit differently.

an altitude of 15,000 feet

step-by-step explanation: