Answer:
A darts player practices throwing a dart at the bull’s eye on a dart board. Her probability of hitting the bull’s eye for each throw is 0.2.
(a) Find the probability that she is successful for the first time on the third throw:
The number F of unsuccessful throws till the first bull’s eye follows a geometric
distribution with probability of success q = 0.2 and probability of failure p = 0.8.
If the first bull’s eye is on the third throw, there must be two failures:
P(F = 2) = p
2
q = (0.8)2
(0.2) = 0.128.
(b) Find the probability that she will have at least three failures before her first
success.
We want the probability of F ≥ 3. This can be found in two ways:
P(F ≥ 3) = P(F = 3) + P(F = 4) + P(F = 5) + P(F = 6) + . . .
= p
3
q + p
4
q + p
5
q + p
6
q + . . . (geometric series with ratio p)
=
p
3
q
1 − p
=
(0.8)3
(0.2)
1 − 0.8
= (0.8)3 = 0.512.
Alternatively,
P(F ≥ 3) = 1 − (P(F = 0) + P(F = 1) + P(F = 2))
= 1 − (q + pq + p
2
q)
= 1 − (0.2)(1 + 0.8 + (0.8)2
)
= 1 − 0.488 = 0.512.
(c) How many throws on average will fail before she hits bull’s eye?
Since p = 0.8 and q = 0.2, the expected number of failures before the first success
is
E[F] = p
q
=
0.8
0.2
= 4.
Given:
value of the test statistic is t20 = 1.95
corresponding p-value of 0.0653 at the 5% significance level
No, I can't conclude that the correlation coefficient differs from zero because the p-value, which is 0.0653 exceeds 0.05.
The correlation coefficient differs from zero when the p-value is less than 0.05.
Answer:
26 = 5 + (r×3)
26 - 5 = 21
21 ÷ 3 =
7
7 is the amount of rides you went on at the fair
U see the box in the triangle is 90 so use it solve it
Answer:
Q1) D Q2) The final statement Q3) first statement Q4) (0,14) and (10,1)
Step-by-step explanation:
Q1) in this D has the most points therefore highest correlation
Q2) there is no correlation because the points cannot form a linear line
Q3) it does not touch all points but is extreamly close ans is therefore considered a correct linear correlation.
Q4) these points have the closest linear correlation
