Solution Found!
Imagine that a friend of yours is
Chapter 7, Problem 13AYU(choose chapter or problem)
Problems 13-16 use the information presented in Examples 1 and 2.
a) Find the probability that your friend is between 5 and 10 minutes late.
(b) It is 10 A.M. There is a 40% probability your friend will arrive within the next_____minutes.
Questions & Answers
QUESTION:
Problems 13-16 use the information presented in Examples 1 and 2.
a) Find the probability that your friend is between 5 and 10 minutes late.
(b) It is 10 A.M. There is a 40% probability your friend will arrive within the next_____minutes.
ANSWER:Answer :
Step 1:
- We take X to be the angle at which the pointer comes to rest, so we use the interval [0, 1] =
[a, b] as its range. Since all angles are equally likely, the probability density function should not depend on x and therefore should be constant. That is, we take f to be uniform f(x)=
The probability of generating a number between 10 and 20 is
Now, P(cX
d) = P(10
X
20) and P(a
X
b) = P(0 ≤ x ≤ 30)
P(cX
d) = Area of shaded rectangle =
Therefore, the probability your friend will be between 10 and 20 minutes late is .
b) Assume that there is a 20% probability of a friend will arrive within the next ‘x’ minutes.
x = 0.2.
x = 0.2
x = 0.230
x = 6.
Therefore, probability of a friend will arrive within the next ‘6’ minutes.