Henry hoards a hundred hens. Every day, each hen lays an egg with probability 0.8 independently of all others. Henry sells each egg for 3 cents, except that on half the days, his dog Barkie breaks half the eggs laid that day (and 1.5 eggs is as sellable as 1), and on the remaining half of the days, Barkie breaks 30 eggs. What is the probability that Henry makes more than a $1.30 today

99.27%

Step-by-step explanation:

We have to:

sample size (n) = 100

p = 0.8

1 egg = 3 * 0.01 = 0.03

eggs = 100 - 30 broken eggs = 70

Let's find the probability of winning more than $ 1.30 today:

p (x> 1.30) = p (z, (x -m) / sd)

average earnings:

per day would be:

m1 = 100 / 1.5 * 0.8 * 0.03

m1 = 1.6

sd1 = (m1 * (1 - p)) ^ (1/2) = (1.6 * (1 - 0.8)) ^ (1/2)

sd1 = 0.566

earnings for broken eggs:

m2 = 70 * 0.8 * 0.03

m2 = 1.68

sd2 = (m2 * (1 - p)) ^ (1/2) = (1.68 * (1 - 0.8)) ^ (1/2)

sd2 = 0.58

Now the total profit would be:

m = m1 + m2 = 1.6 + 1.68

m = 3.28

sd = sd1 ^ 2 + sd2 ^ 2 = 0.566 ^ 2 + 0.58 ^ 2

sd = 0.81

now yes, replacing:

p (x> 1.30) = p (z> (1.3 - 3.28) /0.81)

p (x> 1.30) = p (z> -2.44)

for this z = 0.0073

Therefore the probability would be:

1 - 0.0073 = 0.9927

That is, we would have a 99.27% probability of achieving the goal.

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.

i dont know sorry

step-by-step explanation: