Suppose that in sampling for the population proportion, it is found that 20 out of 100 items are defective. construct a 95% confidence interval for the proportion of defective items in the population

(0.1216,0.2784)

Step-by-step explanation:

The confidence interval for population proportion is given by :-

, where = Sample proportion.

n= sample size.

z* = critical z-value.

Given : sample size = 100

Sample proportion of defective items =

Confidence level =95%

We know that , Critical z-value for 95% confidence interval  = 1.96

Then, the confidence interval for the proportion of defective items in the population will be :-

Hence, the 95% confidence interval for the proportion of defective items in the population =  (0.1216,0.2784)

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.

6, 10

9, -13

12, -21

18, -23

step-by-step explanation:

you just add 6 to the x-coordinate and subtract 10 from the y-coordinate.