b. What is the standard deviation of survival time?
c. What is the probability that an animal survives more than 30 weeks?
Answer:
Step-by-step explanation:
From the given information:
Let X be the random variable;
The mean survival time is E(X):
E(X) = μ
E(X) = ∝β
E(X) = 5 × 10
E(X) = 50
To find the standard deviation, we must first determine the variance:
The standard deviation is:
The standard deviation of survival time = 22.361
(c)
P(X>30) = 1 - P(X ≤ 30)
So, if:
10dy = dx
and limits of y are 0 and 3.
because;
for x = 0
y = 0
For x = 30
y = 10
From (1);
since y = x/β
Since;
Then;
P(X> 30) = 1 - F(3,5)
From the table of incomplete gamma function;
P(X > 30) = 1 - 0.185
P(X > 30) = 0.815
Thus, the probability that an animal survives more than 30 weeks is 0.815
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