Answer:
a) The probaility is 0.333.
b) The probability is 0.125.
c) The volume is 0.512 m3.
Step-by-step explanation:
Organisms are present in ballast water discharged with a concentration of 10 organisms/m3.
That is our rate of the Poisson process
a) The probability of having at least 8 organisms is equal to the sum of the probabilities of having from 0 to 8 organisms:
Note: In this case, the volume V is 1 m3.
b) In this case, the volume is 1.5m3 so we have to multiply the rate by 1.5. Then it becomes:
The standard deviation of this distribution is
We have to calculate the probability of exceeding 19 organisms in 1.5m3:
We have that the probability of having <em>more</em> than 19 org. is equal to <em>one substracting the probability of having equal or less</em> than 19 org:
c) We have to calculate the volume such that there is a probability P=0.994 of having at least one organism in the water. This can be calculated as one less the probability of having zero organisms.
<span>Find the range of the function. f(x) = x^2 + 3
</span>A: (3,infinity)
Answer:
r = ±1/√7
a₁ = 7 − √7
Step-by-step explanation:
The first term is a₁ and the second term is a₁ r.
a₁ + a₁ r = 48/7
The sum of an infinite geometric series is S = a₁ / (1 − r)
a₁ / (1 − r) = 7
Start by solving for a₁ in either equation.
a₁ = 7 (1 − r)
Substitute into the other equation:
7 (1 − r) + 7 (1 − r) r = 48/7
1 − r + (1 − r) r = 48/49
1 − r + r − r² = 48/49
1 − r² = 48/49
r² = 1/49
r = ±1/√7
When r is positive, the first term is:
a₁ = 7 (1 − r)
a₁ = 7 (1 − 1/√7)
a₁ = 7 − 7/√7
a₁ = 7 − √7