Respuesta :
Answer:
Mean: 16
Variance: 3.2
Step-by-step explanation:
For each fish, there are only two possible outcomes. Either they survive, or they do not. The probability of a fish surviving is independent from other fishes. So we use the binomial probability distribution to solve this question.
Binomial probability distribution
Probability of exactly x sucesses on n repeated trials, with p probability.
Can be approximated to a normal distribution, using the expected value and the standard deviation.
The expected value of the binomial distribution is:
[tex]E(X) = np[/tex]
The variance of the binomial distribution is:
[tex]V(X) = np(1-p)[/tex]
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.
This means that 80% survive, so [tex]p = 0.8[/tex]
The mean is:
[tex]E(X) = np = 20*0.8 = 16[/tex]
The variance is:
[tex]V(X) = np(1-p) = 20*0.8*0.2 = 3.2[/tex]
Answer:
mean=16
Variance=3.2
Step-by-step explanation:
P(lethal)=P(not survive)=0.20
P( not lethal)=P(survive)=1-0.2=0.8
The specified scenario indicates binomial distribution because
i) There are two possible outcomes lethal or not lethal.
ii) Probability of not lethal/survive remains constant on each trail.
iiI) The experiment is repeated fixed number of times n=20.
iv) The trails are independent.
The mean for binomial distribution is
E(x)=np
Here, n=20 and p=0.8
E(x)=20*0.8
E(x)=16
The variance of binomial distribution is
V(x)=npq
q=1-p=1-0.8=0.2
So,
V(x)=20*0.8*0.2
V(x)=3.2
