A binomial experiment has 6 trials in which p = 0.85. what is the probability of getting at least 4 successes?
1 answer:
By applying binomial probability, the probability of getting at least four (4) successes is 0.9527.
<h3>How to determine the probability?</h3>In order to determine the probability of getting at least four (4) successes, we would apply binomial probability equation:
The probability of getting at least four (4) successes is given by:
P(x ≥ 4) = P(4) + P(5) + P(6)
Substituting the given parameters into the equation, we have;
P = ⁶C₄ × (0.85)⁴ × (0.15)³ + ₅C₆ × (0.85)⁵ × (0.15) + ⁶C₆ × (0.85) × (0.15)⁶
P = 0.17618 + 0.39933 + 0.37715
P = 0.9527.
Read more on probability here: brainly.com/question/25870256
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The first and second coordinate points of the sine graph are;
(0, 20) and (2, 22)
<h3>Sine Graph expression</h3>
The general formula we will use to plot the graph is;
y = [Asin (2πx/t)] + ∅ (Note that sin is in radians)
where;
A is amplitude
t is period
∅ is phase shift
We are told that the buoy bobs up and then down 2 meters from the ocean's depth. This means that;
Amplitude; A = 2
Now, Four seconds pass from the time the buoy is at its highest point to when it is at its lowest point. Thus;
Period = 2 * 4 = 8 seconds
Assume at x = 0, the buoy is at normal ocean depth. Thus;
Phase shift; ∅ = 20
Thus, we have;
y = [2sin((2πx/8)] + 20
At x = 0, we have;
y = [2sin((2π*0/8)] + 20
y = 0 + 20
y = 20
Thus, first point is; (0, 20)
Since the second point must be a maximum or minimum value on the graph closest to the first point, then we put 2 for x to get the coordinate of the second point;
y = [2sin((2π*2/8)] + 20
y = [2sin((2π*2/8)] + 20
y = [2sin(π/2)] + 20
In radians, sin(π/2) = 1. Thus;
y = (2 * 1) + 20
y = 22
Second point is (2, 22)
Using the first and second point coordinates, we will use sine tool to graph the function as attached below.
Read more about sine graph at; brainly.com/question/18055768
