Please help with the following statistics question A cordles

Please help with the following statistics question,

A cordless drill has several torque settings for driving different screws into different materials. A manufacturer models the torque setting required for a randomly selected task with a probability distribution given by p(x) = (x - 12)^2 / 247 x = 1, 5, 10, 15, 20 Find the probability that the torque setting is at least 5 but less than 20. Find the probability that the torque setting is more than 10.

Solution

a)

P(at least 5 but less than 20) = P(5) + P(10) + P(15)

= (5-12)^2/247 + (10-12)^2/247 + (15-12)^2/247

= 0.251012146 [answer]

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b)

P(more than 10) = P(15) + P(20)

=(15-12)^2/247 + (20-12)^2/247

= 0.295546559 [answer]