Question

the city of franklin runs an after - school arts program for children aged 6 to 10. suppose a child from the program is randomly selected. let x be the age (in years) of the selected child. here is the probability distribution of x.
for parts (a) and (b) below, find the probability that the randomly selected child has the age described.
(a) older than 7:
(b) younger than 9:

Explanation:

Step1: Find probability for part (a)

For a child to be older than 7, \(x = 8,9,10\).
\(P(X>7)=P(X = 8)+P(X = 9)+P(X = 10)\)
\(P(X>7)=0.18 + 0.25+0.26\)

Step2: Calculate the sum for part (a)

\(P(X>7)=0.69\)

Step3: Find probability for part (b)

For a child to be younger than 9, \(x = 6,7,8\).
\(P(X<9)=P(X = 6)+P(X = 7)+P(X = 8)\)
\(P(X<9)=0.16+0.15 + 0.18\)

Step4: Calculate the sum for part (b)

\(P(X<9)=0.49\)

Answer:

(a) \(0.69\)
(b) \(0.49\)