a pitcher pitches a ball to a hitter. the ball is hit towards center field hits the center field fence, then drop to the ground.
1 answer:
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<h2>Answer:</h2>
Shown in the figure below.
<h2>Step-by-step explanation:</h2>We have the equation:
So this is a sine function shifted 2 units upward. The midline of this function is . From the figure below, you can see that the first point lies on the midline at the pojnt
. The second point lies on
, which is a maximum point and is the closest point to the first one.
The probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%
The Mean of the uniform distribution for an interval from a to b is given by the formula :
μ =
Here, the given interval is from 7.5 to 10.5 gallons per minute, that means a= 7.5 and b= 10.5
So, Mean(μ) =
Now, the standard deviation of the uniform distribution is given by the formula:
σ =
So, the standard deviation(σ) =
As we need to find the probability that between 8.0 gallons and 9.0 gallons are pumped, so now we will find z-score for both 8.0 and 9.0
The formula for z-score: z = (X - μ)/σ
So, z(X= 8.0) =
and z(X= 9.0) =
Now according to the z-score table, P(z=-1.1547) = 0.1251 and P(z=0) = 0.5
So, P(8.0 < x < 9.0)
= P(-1.1547 < z <0)
= 0.5 - 0.1251
= 0.3749
= 37.49%
Thus, the probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%
