lexiscaraballo12
17.06.2020 •
Mathematics
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
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Ответ:
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.
Ответ:
s=7.5
Step-by-step explanation:
I hope this help you