Percent of red lights last between 2.5 and 3.5 minutes is 95.44% .
<u>Step-by-step explanation:</u>
Step 1: Sketch the curve.
The probability that 2.5<X<3.5 is equal to the blue area under the curve.
Step 2:
Since μ=3 and σ=0.25 we have:
P ( 2.5 < X < 3.5 ) =P ( 2.5−3 < X−μ < 3.5−3 )
⇒ P ( (2.5−3)/0.25 < (X−μ)/σ < (3.5−3)/0.25)
Since, Z = (x−μ)/σ , (2.5−3)/0.25 = −2 and (3.5−3)/0.25 = 2 we have:
P ( 2.5<X<3.5 )=P ( −2<Z<2 )
Step 3: Use the standard normal table to conclude that:
P ( −2<Z<2 )=0.9544
Percent of red lights last between 2.5 and 3.5 minutes is 
% .
<span>Point B has coordinates (3,-4) and lies on the circle. Draw the perpendiculars from point B to the x-axis and y-axis. Denote the points of intersection with x-axis A and with y-axis C. Consider the right triangle ABO (O is the origin), by tha conditions data: AB=4 and AO=3, then by Pythagorean theorem:
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{Note, that BO is a radius of circle and it wasn't necessarily to use Pythagorean theorem to find BO}
<span>The sine of the angle BOA is</span>
Since point B is placed in the IV quadrant, the sine of the angle that is <span> drawn in a standard position with its terminal ray will be </span>
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.
Answer: 1
B is the center of a circle of radius 1. A and C are on the circle 100 degrees apart. So arc AC is 100 degrees. Arc AC the long way around is 360-100=260 degrees. That means any point D on arc AC will subtend a 130 degree angle. BD is a radius for all of those, and the radius is 1.
Cos y = 16 / 17.89 = 0.8944
y = cos^-1 (0.8944) = 26.57°
tan 26.57 = BA / 17.89
BA = 17.89 tan 26.57 = 8.95
tan x = 17.89 / 8.95 = 1.999
x = arctan 1.999 = 63.43
sin x = sin 63.43 = 0.8944
Answer:
P(X=2)=0.0446
Step-by-step explanation:
If X follows a Poisson distribution, the probability p to have x pits in 1 cm2 is calculated as:
Where m is the mean of pits per cm2, so, replacing m by 6 pits per cm2, we get that the probability is equal to:
Now, the probability P(x=2) that there are 2 pits in a 1 cm2 is calculated as:
