"Emergency Please Help"!!!!!
A bus is scheduled to stop at a certain bus stop every 45 minutes. At the end of the day, buses still
stop after every 45 minutes, but because delays often occur earlier in the day, the bus is never early
and likely to be late. The director of the bus line claims that the length of time a bus is late is
uniformly distributed over the interval 0 to 35 minutes. If the director's claim is true, what is the
probability that the last bus on a given day will be more than 22 minutes late?
A) 0.78
B) 0.4
C) 0.37
D) 0.63
(35 -22)/35 = ?
thank you PsyDAG
To find the probability that the last bus on a given day will be more than 22 minutes late, we need to calculate the area under the probability density function (PDF) of the uniform distribution from 22 minutes to 35 minutes.
The formula for the PDF of a uniform distribution is:
f(x) = 1 / (b - a)
Where a is the lower limit (0 minutes in this case) and b is the upper limit (35 minutes).
Let's calculate the probability using this formula:
P(last bus > 22 minutes late) = ∫[22, 35] f(x) dx
Using the formula for the PDF, we have:
P(last bus > 22 minutes late) = ∫[22, 35] 1 / (35 - 0) dx
Simplifying the expression:
P(last bus > 22 minutes late) = ∫[22, 35] 1 / 35 dx
Integrating the expression:
P(last bus > 22 minutes late) = [x / 35] from 22 to 35
Evaluating the integral:
P(last bus > 22 minutes late) = [(35 / 35) - (22 / 35)]
P(last bus > 22 minutes late) = (13 / 35)
Calculating the value:
P(last bus > 22 minutes late) ≈ 0.3714
Therefore, the probability that the last bus on a given day will be more than 22 minutes late is approximately 0.3714.
Thus, the correct answer is C) 0.37.
To find the probability that the last bus on a given day will be more than 22 minutes late, we need to use the uniform distribution.
The uniform distribution means that all values within a given range have an equal probability of occurring. In this case, the range is from 0 to 35 minutes.
To find the probability that the bus is more than 22 minutes late, we need to calculate the proportion of the range that is greater than 22.
The total range is 35 minutes, and the portion that is greater than 22 minutes is (35 - 22) = 13 minutes.
So, to find the probability, we divide the portion that is greater than 22 by the total range.
Probability = (portion greater than 22) / (total range)
Probability = 13 / 35 = 0.37
Therefore, the probability that the last bus on a given day will be more than 22 minutes late is 0.37.
Hence, the correct answer is C) 0.37.