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  • 11. The mean and variance of a random variable  are 20 and 4 respectively. Find the probability t

11. The mean and variance of a random variable \mathrm{X} are 20 and 4 respectively. Find the probability that \mathrm{X}  takes a value between 15 and 25.

Option: 1

0.987


Option: 2

0.912


Option: 3

0.844


Option: 4

0.721


Answers (1)

best_answer

Solution: Let \mathrm{X}  be a random variable with mean 20 and variance 4 .
Then, the probability that \mathrm{X}  takes a value between 15 and 25 is given by:
\mathrm{P}(15<\mathrm{X}<25)=\mathrm{P}(\mathrm{Z}<(25-20) / 2)-\mathrm{P}(\mathrm{Z}<(15-20) / 2)
where \mathrm{Z}  is a standard normal variable.
\mathrm{=P(z<2.5)-P(Z<-2.5) }
\mathrm{ =0.993807-0.006206 }
\mathrm{ =0.987591 . }

Therefore, the probability that \mathrm{ X . } takes a value between 15 and 25 is \mathrm{ 0.987591 }

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Pankaj

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