Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility. Suppose that the density curve has height f(x) above the value x. Use the fact that the area of a triangle = 1/2(base) (height) to calculate each of the probabilities below: - ƒ (x) = { 2 (¹ − x) (a) P(x < 1/4) = (b) P(x≤ 1/4) = (c) P(x < 1/8) = 0 ≤ x ≤ 1 otherwise Density 2 L (d) P(1/8

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7.3.3

Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility. Suppose that
the density curve has height f(x) above the value x. Use the fact that the area of a triangle
each of the probabilities below:
1/2(base) (height) to calculate
ƒ (x) = { 2 (¹
2 (1-x)
(a) P(x < 1/4) =
(b) P(x ≤ 1/4) =
(c) P(x < 1/8) =
0≤x≤ 1
otherwise
Density
(d) P(1/8 < x < 1/4) =
=
2
X
Tons
(e) The probability that gravel sold exceeds 1/4 ton.
P (sales exceed 1/4 a ton)
=
(f) The probability that gravel sold is at least 1/8 ton.
P (sales is at least 1/8 ton )
=
Transcribed Image Text:Let x denote the amount of gravel sold (in tons) during a randomly selected week at a particular sales facility. Suppose that the density curve has height f(x) above the value x. Use the fact that the area of a triangle each of the probabilities below: 1/2(base) (height) to calculate ƒ (x) = { 2 (¹ 2 (1-x) (a) P(x < 1/4) = (b) P(x ≤ 1/4) = (c) P(x < 1/8) = 0≤x≤ 1 otherwise Density (d) P(1/8 < x < 1/4) = = 2 X Tons (e) The probability that gravel sold exceeds 1/4 ton. P (sales exceed 1/4 a ton) = (f) The probability that gravel sold is at least 1/8 ton. P (sales is at least 1/8 ton ) =
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