The weight of potato chips in a medium-size bag is stated to be 10 ounces the amount that the packaging machine puts in these bags is believed to have a normal model with mean 10.2 and standard deviation 0.12 ounces. What's the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces?

The probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

Step-by-step explanation:

Let X = weight of potato chips in medium size bag.

The random variable X follows a Normal distribution with mean, μ = 10.2 ounces and standard deviation, σ = 0.12 ounces.

A sample of n = 24 bags of chips is selected.

Compute the probability that the mean weight of these 24 bags is less than 10 ounces as follows:

Thus, the probability that the mean weight of a 24-bag case of potato chips is below 10 ounces is approximately 0.

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.

its 4 because 2 times 2 is 4, if you double the number two you get four