Let x be the amount of time (in minutes) that a particular San Francisco commuter must wait for a BART train. Suppose that the d
ensity curve is as pictured below (a uniform distribution):
(a) What is the probability that x is less than 11 min? more than 14 min? P (x is less than 11 minutes) = P (x is more than 14 minutes) =
(b) What is the probability that x is between 8 and 13 min? P (x is between 8 and 13 minutes) =
(c) Find the value c for which P(x < c) = .8. c = mins You may need to use the appropriate table in Appendix A to answer this question.
(a) What is the probability that x is less than 11 min? more than 14 min? P (x is less than 11 minutes) = P (x is more than 14 minutes) =
(b) What is the probability that x is between 8 and 13 min? P (x is between 8 and 13 minutes) =
(c) Find the value c for which P(x < c) = .8. c = mins You may need to use the appropriate table in Appendix A to answer this question.
2 answers:
Your question is not complete, as you have not provided the uniform distribution, please see attached to view the distribution, as (0, 0.05) and (20, 0.05).
Answer:
A. I) 0.45
II) 0.3
B) 0.25
C) 4
Step-by-step explanation:
The probability will be calculated using (base)(height). Since the height is static at 0.05, which is the density and the base is the X values. Therefore the probability will be a function of minutes which is the X values.
A.
I) The probability that X is less than 11 minutes (X<11)
(0.05)(20-11)
0.05 × 9= 0.45
II) The probability that X is greater than 14 minutes is (X>14)
(0.05)(20-14)
0.05 × 6 = 0.3
B.
The probability that X is between 8 and 13 minutes (8<X<13)
(0.05)(13-8)
0.05 × 5 = 0.25
C.
(X<c)= 0.8 find the value of c
Since the probability is (base)(height)
Therefore;
(0.05)(20-c) = 0.8
Multiply bracket
1-0.05c = 0.8
1 - 0.8 = 0.05c
0.2 = 0.05c
C = 0.2 ÷ 0.05
C = 4
You might be interested in