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  • 10. The mean and variance of a random variable   are 10 and 25 respectively. Find the probability

10. The mean and variance of a random variable \mathrm{X}  are 10 and 25 respectively. Find the probability that \mathrm{X}  takes a value less than 5 .

Option: 1

0.124


Option: 2

0.158


Option: 3

0.136


Option: 4

0.186


Answers (1)

best_answer

 Let \mathrm{X} be a random variable with mean 10 and variance 25.

Then, the probability that \mathrm{X}  takes a value less than 5 is given by:
\mathrm{ P(X<5)=P(Z<(5-10) / 5) }
where \mathrm{Z}  is a standard normal variable.
\mathrm{ =P(Z<-1) }
\mathrm{ =0.158655 . }

Therefore, the probability that \mathrm{ X }  takes a value less than 5 is 0.158655 .

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