Answer:
Step-by-step explanation:
Given that room temperature X in centigrade follows Uniform distribution in the interval (-6,6)
a) [tex]P(X<0) = P(-6<x<0) = 0.50[/tex]
b) [tex]P(-3<x<3) =\frac{3-(-3)}{6-(-6)} \\=0.50[/tex]
c) [tex]P(-4<x<5) =\frac{5-(-4)}{6-(-6)}\\=0.75[/tex]
d) [tex]P(k<x<k+4) =\frac{k+4-(k)}{6-(-6)}\\=0.3333[/tex] (because k andk+4 are within -6 and 6)
Based on the calculations, P(X < 0) is equal to 0.5.
Since the given data has a uniform distribution with A = −6 and B = 6, the probability is given by this formula:
[tex]f(x)=\frac{1}{B-A} \\\\f(x)=\frac{1}{6-(-6)}\\\\f(x)=\frac{1}{12}\\\\f(x)=0.08[/tex]
a. To compute P(X < 0):
[tex]P(X < 0)=P(-6 < X < 0)\\\\P(-6 < X < 0)=\frac{0-(-6)}{6-(-6)} \\\\P(-6 < X < 0)=\frac{6}{12}[/tex]
P(-6<X < 0) = 0.5.
b. To compute P(−3 < X < 3):
[tex]P(-3 < X < 3)=\frac{3-(-3)}{6-(6)} \\\\P(-3 < X < 3)=\frac{6}{12}[/tex]
P(-3 < X < 3) = 0.5.
c. To compute P(-4 ≤ X ≤ 5):
[tex]P(-4 \leq X \leq 5)=\frac{5-(-4)}{6-(6)} \\\\P(-4 \leq X \leq 5)=\frac{9}{12}[/tex]
P(-4 ≤ X ≤ 5) = 0.75.
d. To compute P(k < X < k + 4):
Note: k satisfies [tex]-6 < k < k + 4 < 6[/tex] and as such k and [tex]k+4[/tex] are both within -6 and 6.
[tex]P(k < X < k+4)=\frac{k+4-(k)}{6-(6)} \\\\P(-3 < X < 3)=\frac{6+4-6}{12}\\\\P(-3 < X < 3)=\frac{4}{12}[/tex]
P(-3 < X < 3) = 0.33.
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