A spinner is divided into three parts, numbered from 1 to 3 as shown below. When

Question

A spinner is divided into three parts, numbered from 1 to 3 as shown below. When this spinner is spun, the arrow randomly points to one of the numbers. Suppose the spinner is spun once and the random variable X is deed as the appeared number. Create the probability distribution table of X and fill it with appropriate probabilities. Given that the probability that a new hospital machine will fail on startup is 1%, assuming startups are independent, what is the probability that the machine will fail on the fourth startup? What is the mean and what is the standard deviation?

Explanation / Answer

here as probabilty is proportion to area enclosed by regions

let total area is A.

hence area enclosed by 1 =A/4

area enclosed by 2=A/2

area enclosed by 3=A/4

hence

2) this is geomteric distribution

probability that m/c wil fail on fourth startup =P(it passess on first 3* failed on 4th attempt)

=(1-0.01)3*0.01=0.009703

mean =1/p=1/0.01=100

std deviation =((1-p)/p2)1/2 =99.5

x 1 2 3 P(X) 0.25 0.5 0.25

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