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  • The mean and variance of a random variable   are 25 and 16 respectively. Find the probability tha

The mean and variance of a random variable \mathrm{X}  are 25 and 16 respectively. Find the probability that \mathrm{X}  takes a value more than 35 .

Option: 1

0.009


Option: 2

0.001


Option: 3

0.004


Option: 4

0.006


Answers (1)

best_answer

Solution: Let \mathrm{X}  be a random variable with mean 25 and variance 16.

Then, the probability that \mathrm{X}  takes a value more than 35 is given by:
\mathrm{ P(X>35)=P(Z>(35-25) / 4) }
where \mathbf{Z}  is a standard normal variable.
=\mathrm{P}(\mathrm{Z}>2.5) \\
=1-0.993807
=0.006193 .

Therefore, the probability that \mathrm{X}  takes a value more than 35 is 0.006193 .

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