Answer:
-44
Step-by-step explanation:
Answer:
91/216
Step-by-step explanation:
The probability of getting a 4 in the first three rolls is 1 minus the probability of not getting a 4 on any of the rolls.
P(at least one 4) = 1 − P(no 4s)
P(at least one 4) = 1 − (5/6)³
P(at least one 4) = 91/216
Alternatively, you can calculate it this way.
The probability of getting a 4 on the first roll is 1/6.
The probability of getting a 4 on the second roll is (5/6) (1/6) = 5/36.
The probability of getting a 4 on the third roll is (5/6) (5/6) (1/6) = 25/216.
The probability of any of the three events is 1/6 + 5/36 + 25/216 = 91/216.
Given that percent of computer infected which is found by quality control inspector = 1.3%
Total number of computers = 1500
Now we have to find the number of Defective computer. To find that we will just need to find the product of given defective percent by the total number of computers.
Total number of defective computers = 1.3% of 1500
Total number of defective computers = 0.013* 1500
Total number of defective computers = 19.5
Hence final answer is approx 20 computers.
Step-by-step explanation:
(a) ∫₋ₒₒ°° f(x) dx
We can split this into three integrals:
= ∫₋ₒₒ⁻¹ f(x) dx + ∫₋₁¹ f(x) dx + ∫₁°° f(x) dx
Since the function is even (symmetrical about the y-axis), we can further simplify this as:
= ∫₋₁¹ f(x) dx + 2 ∫₁°° f(x) dx
The first integral is finite, so it converges.
For the second integral, we can use comparison test.
g(x) = e^(-½ x) is greater than f(x) = e^(-½ x²) for all x greater than 1.
We can show that g(x) converges:
∫₁°° e^(-½ x) dx = -2 e^(-½ x) |₁°° = -2 e^(-∞) − -2 e^(-½) = 0 + 2e^(-½).
Therefore, the smaller function f(x) also converges.
(b) The width of the intervals is:
Δx = (3 − -3) / 6 = 1
Evaluating the function at the beginning and end of each interval:
f(-3) = e^(-9/2)
f(-2) = e^(-2)
f(-1) = e^(-1/2)
f(0) = 1
f(1) = e^(-1/2)
f(2) = e^(-2)
f(3) = e^(-9/2)
Apply Simpson's rule:
S = Δx/3 [f(-3) + 4f(-2) + 2f(-1) + 4f(0) + 2f(1) + 4f(2) + f(3)]
S ≈ 2.5103
