The average commute to work (one way) is 25 minutes according to the 2005 American Community Survey. If we assume that commuting times are normally distributed and that the standard deviation is 6.1 minutes, calculate the probability that a randomly selected commuter spends for the following cases. 1. More than 31 minutes commuting one way.
2. Less than 8 minutes commuting one way.

1. 0.1635

2. 0.0026

Step-by-step explanation:

The computation of the probability in the following cases are as follows:

1.

Given that

Mean = 25 minutes

ANd, the standard deviation is 6.1 minutes

So here the z score would be

= (31 - 25) ÷(6.1)

= 0.98

Now the probability is

= P(Z>0.98)

= 0.1635

2. the z score would be

= (8 - 25) ÷(6.1)

= -2.79

Now the probability is

= P(Z<-2.79)

= 0.0026

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.

the answer is 54 sq. ft. i just did this question, on odyssey ware, and it was right. make brainliest.