Question

a carnival spinner has unequal sections labeled 3 through 8. let x be the number shown on the spinner when it is spun. here is the probability distribution of x.
for parts (a) and (b) below, find the probability that the number described is shown on a random spin.
(a) less than or equal to 4:
(b) higher than 6:

Explanation:

Step1: Find probability for part (a)

For \(x = 3\), \(P(X = 3)=0.27\); for \(x = 4\), \(P(X = 4)=0.18\).
Use formula \(P(X\leq4)=P(X = 3)+P(X = 4)\)
\(P(X\leq4)=0.27 + 0.18\)

Step2: Calculate the sum for part (a)

\(0.27+0.18 = 0.45\)

Step3: Find probability for part (b)

For \(x = 7\), \(P(X = 7)=0.13\); for \(x = 8\), \(P(X = 8)=0.12\).
Use formula \(P(X>6)=P(X = 7)+P(X = 8)\)
\(P(X>6)=0.13 + 0.12\)

Step4: Calculate the sum for part (b)

\(0.13+0.12=0.25\)

Answer:

(a) \(0.45\)
(b) \(0.25\)