Answer: The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is 0.596
Step-by-step explanation:
Since the weights of catfish are assumed to be normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = weights of catfish.
µ = mean weight
σ = standard deviation
From the information given,
µ = 3.2 pounds
σ = 0.8 pound
The probability that a randomly selected catfish will weigh between 3 and 5.4 pounds is is expressed as
P(x ≤ 3 ≤ 5.4)
For x = 3
z = (3 - 3.2)/0.8 = - 0.25
Looking at the normal distribution table, the probability corresponding to the z score is 0.401
For x = 5.4
z = (5.4 - 3.2)/0.8 = 2.75
Looking at the normal distribution table, the probability corresponding to the z score is 0.997
Therefore,.
P(x ≤ 3 ≤ 5.4) = 0.997 - 0.401 = 0.596
Point D, as shown i the figure, is the intersection of the angle bisectors. This point is the Incircle, or the center of the inscribed circle.
All 3 angle bisectors meet at D, so drawing the angle bisector of C is useless. (Thus step 4 is not the one).
Since we have the center of the inscribed circle, we want to open the compass so that it touches all 3 sides at one point only, that is, we want the 3 sides to be tangent to this circle.
The segments joining the tangency points and D are 3 radii of the circle. We know that a radius is perpendicular to the tangent it touches.
Thus, we need to draw an altitude from D to any of the sides.
Answer: 1
