In a biomedical research study, it was determined that the survival time, in weeks, of an animal subjected to a certain exposure of gamma radiation has a gamma distribution with α= 5 and β=10. a. What is the mean survival time of a randomly selected animal of the type used in the experiment?
b. What is the standard deviation of survival time?
c. What is the probability that an animal survives more than 30 weeks?

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

the smallest possible measurement of the width is 14 feet

step-by-step explanation:

let's assume length of parallelogram is 'l'

width of parallelogram is 'w'

the perimeter of a parallelogram must be no less than 40 feet

so, we get

we are given

length of parallelogram is 6 feet

so,

l=6

we can plug it

now, we can solve for w

subtract both sides by 12

divide both sides by 2

and we get

so,

the smallest possible measurement of the width is 14 feet

answer is 12345678900987654321234567890987654321

step-by-step explanation: