Answer:
(a) 35 heads correspond to -3 on the standard scale.
(b) z = 2.4 corresponds to 62 heads on the number of heads scale.
Step-by-step explanation:
(a) If we flip a fair coin once, probability of getting head = 0.5
If we flip a fair coin 100 times, mean number of heads = 100(0.5) = 50
If there are N draws with a P probability of success, the standard deviation (SD) is given as:
Here, the probability of getting a head (P) is 0.5 while the number of draws (N) is 100. So,
SD = 5
The standard scale value is: (35 - 50) / 5 = -3
Hence, 35 heads correspond to -3 on the standard scale.
(b) The standard scale value is 2.4 and we need to find the number of heads.
(X - 50) / 5 = 2.4
X - 50 = 12
X = 62
Hence, z = 2.4 on the standard scale corresponds to 62 on the number of heads scale.
Answer:
P(4≤x≤7) = 2/3
Step-by-step explanation:
We'll begin by obtaining the sample space (S) i.e possible outcome of rolling both dice at the same time. This is illustrated below:
1,1 1,2 1,3 1,4 1,5 1,6
2,1 2,2 2,3 2,4 2,5 2,6
3,1 3,2 3,3 3,4 3,5 3,6
4,1 4,2 4,3 4,4 4,5 4,6
5,1 5,2 5,3 5,4 5,5 5,6
6,1 6,2 6,3 6,4 6,5 6,6
Adding the outcome together, the sample space (S) becomes:
2 3 4 5 6 7
3 4 5 6 7 8
4 5 6 7 8 9
5 6 7 8 9 10
6 7 8 9 10 11
7 8 9 10 11 12
Next, we shall obtain the event of 4≤x≤7. This is illustrated below:
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
4 5 6 7
Finally, we shall determine P(4≤x≤7). This can be obtained as follow:
Element in the sample space, n(S) = 36
Element in 4≤x≤7, n(4≤x≤7) = 24
Probability of 4≤x≤7, P(4≤x≤7) = ?
P(4≤x≤7) = n(4≤x≤7) / nS
P(4≤x≤7) = 24/36
P(4≤x≤7) = 2/3
Answer:
Step-by-step explanation:
This arc has the same measurement as the central angle. The central angle is LON where O is the center of the circle.
Point M forms an angle that is 1/2 the central angle when M is on the circumference and opposite the 150o angle. Therefore M is the vertex of a 75 degree angle.
76x - 1 = 75 Add 1 to both sides.
76x = 76 Divide by 76
x = 1
Answer:
Step-by-step explanation:
