Solution Found!
A particular sale involves four items randomly selected
Chapter 3, Problem 58E(choose chapter or problem)
A particular concentration of a chemical found in polluted water has been found to be lethal to
20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a
tank containing this concentration of chemical in water.
a Find the probability that exactly 14 survive.
b Find the probability that at least 10 survive.
c Find the probability that at most 16 survive.
d Find the mean and variance of the number that survive.
Questions & Answers
QUESTION:
A particular concentration of a chemical found in polluted water has been found to be lethal to
20% of the fish that are exposed to the concentration for 24 hours. Twenty fish are placed in a
tank containing this concentration of chemical in water.
a Find the probability that exactly 14 survive.
b Find the probability that at least 10 survive.
c Find the probability that at most 16 survive.
d Find the mean and variance of the number that survive.
ANSWER:
Answer:
Step 1 of 1:
A sale has mentioned that 4 items randomly selected from a large lot that is known to contain 10% defectives.
Let denote the number of defectives among the 4 sold item. The purchaser of the items will return the defectives for repair, and the repair cost is given by
.
We need to find the expected repair cost .
Here follows the binomial distribution, hence we can write mean and variance of the binomial distribution.
The mean of a random variable with a binomial distribution is,