The PDF for the wait time (denoted by the random variable X) is
where λ = 1/75. We want to find Pr[X > 70 | X ≥ 40]. Pierre has already been waiting for 40 min, so if he waits another 30 min he will have waited for a total of 70 min.
By definition of conditional probability,
Pr[X > 70 | X ≥ 40] = Pr[X > 70 and X ≥ 40] / Pr[X ≥ 40]
If X > 70, then automatically X ≥ 40 is satisified, so the right side reduces to
Pr[X > 70 | X ≥ 40] = Pr[X > 70] / Pr[X ≥ 40]
Use the PDF or CDF to find the remaining probabilities. For instance, using the PDF,
Or, using the CDF,
Similarly, you'll find that Pr[X ≥ 40] ≈ 0.5866.
It follows that
Pr[X > 70 | X ≥ 40] ≈ 0.3932 / 0.5866 ≈ 0.6703
Answer:
Choice A
Step-by-step explanation:
You take the x value and plug it into the formula to see if the answer lines up with the table
Answer:
$3190.00
Step-by-step explanation:
Answer:
-12
12
Step-by-step explanation:
(-3) * 4
Remove parentheses. ( -a) = -a
= -3 * 4
Multiply the numbers: 3 * 4 = 12
= -12
(4) * 3
Multiply the numbers.
4 * 3 = 12
= 12