Suppose you were interested in how good someone was at surfing. You find that, 54% of the
time, they successfully do a particular trick. 8% of the time, they do the trick with small
mistakes. The rest of the time they fail to do the trick at all.
- In any one attempt to do the trick, what is the probability that this person will complete
it, either perfectly or with small mistakes?
- Assume that surfing success rate in each attempt to do the trick is independent of
success in any other attempt to do the trick. Suppose you were interested in how many
times this surfer would successfully complete the trick (with no mistakes or with minor
mistakes) in four upcoming attempts. What is the probability that the surfer fails to
complete the trick in the first attempt and then completes it with no mistakes in the
next three attempts?
- What is the probability that the surfer fails to complete the trick in all four attempts
(they do not do the trick at all in any of the events)?
-What is the probability that the surfer successfully completes the trick (with or without
mistakes) in at least one of the four attempts?
-Suppose the proportion of trick success rate (completing without mistakes or with small
mistakes) was distributed on a normal curve with a mean of 0.68 and a standard
deviation of 0.07. What percent of surfers would you expect to have fewer successful
attempts (no mistakes or with small mistakes) than the surfer you watched?
1) Let p = P(surfer completes the trick successfully or with
small
mistakes)
p = 0.54 +
0.08
p = 0.62
P(person will complete the trick, either perfectly or with small
mistakes in any one attempt) =
0.62
2) s = 0.54 Probability of success without any
mistakes
p = 0.62 Probability of success with or without
mistakes
q = 1 - 0.62 = 0.38 Probability of failure in a single
attempt
P(surfer fails to complete the trick in the first attempt and then
completes it with no mistakes in the next three
attempts)
= q * s * s *
s
= 0.38 * 0.54 * 0.54 *
0.54
= 0.0598
P(surfer fails to complete the trick in the first attempt and then
completes it with no mistakes in the next three attempts) =
0.0598
3) P(surfer fails to complete the trick in all 4
attempts)
= q * q * q *
q
= 0.38 * 0.38 * 0.38 *
0.38
= 0.0209
P(surfer fails to complete the trick in all 4 attempts) =
0.0209
4) P(surfer successfully completes in atleast 1 of the 4
attempts)
= 1 - P(surfer does not successfully complete in all of the 4
attempts)
= 1 - 0.0209 (0.0209 is the probability calculated in
(3))
=
0.9791
P(surfer successfully completes in atleast 1 of the 4 attempts) =
0.9791
5) p = 0.62 which is the probability of success of our
surfer
Let X be the proportion of trick success rate
X follows normal distribution with mean = 0.68 and standard
deviation =
0.07
We have to find percentage of surfers with success rate less than
0.62
P(X <
0.62)
We use Excel function NORM.DIST to find the
probability
P(X < 0.62) = NORM.DIST(0.62, 0.68, 0.07,
TRUE)
P(X < 0.62) =
0.1957
Percentage of surfers with fewer successful attempts than our
surfer =
19.57%
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