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.

step-by-step explanation:

let

we know that

the y-intercept is the y-coordinate of the point when the value of x is equal to zero

so

the y-coordinate of the point a is the y-intercept

the answer part a) is

the value of y-intercept is

part b) find the slope m

we know that

the value of the slope is equal to

substitute the values

therefore

the answer part b) is

the value of the slope is equal to

the general answer is

the slope is

the value of y-intercept is