Part B
2 answers:
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Answer:
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
Step-by-step explanation:
In a Poisson distribution, the probability that X represents the number of successes of a random variable is given by the following formula:
In which
x is the number of sucesses
e = 2.71828 is the Euler number
is the mean in the given interval. The variance is the same as the mean.
Average rate of 56 calls per hour:
This means that , in which n is the number of hours.
Find the average and standard deviation of the number of service calls in a 15-minute period.
15 minute is one fourth of a hour, which means that . So
The variance is also 14, which means that the standard deviation is
The average number of service calls in a 15-minute period is of 14, with a standard deviation of 3.74.
I hope this answers your question.
Answer:
The area of the triangle formed by origin, and the points (4,5) and (-2,5) will be 15 sq. units.
Step-by-step explanation:
The two parabolas are and y = x² - 2x - 3.
Now, solving those two equations we will get the points of intersection.
So,
⇒ - (x - 1)² + 24 = 3x² - 6x - 9
⇒ -x² + 2x - 1 + 24 = 3x² - 6x - 9
⇒ 4x² - 8x - 32 = 0
⇒ x² - 2x - 8 = 0
⇒ x² - 4x + 2x - 8 = 0
⇒ (x - 4)(x + 2) = 0
So, x = 4 or - 2.
Now, for x = 4 , y = 4² - 2(4) - 3 = 5 and the point of intersection is (4,5).
Or, for x = - 2, y = (- 2)² - 2(- 2) - 3 = 5 and the point of intersection is (-2,5).
Now, points (4,5) and (-2,5) make a straight line parallel to the x-axis at a perpendicular distance of 5 units from origin and its length is (4 - (- 2)) = 6 units.
So, the area of the triangle formed by origin, and the points (4,5) and (-2,5) will be = 0.5 × 5 × 6 = 15 sq. units. (Answer)