Normal mixture probability

[mikesiberia]

A variable X is a mixture of two normal variables: the first one has expectation 3 and standard deviation 1, the second one has expectation 1 and standard deviation 2. The mixture law is (0.5,0.5)
The probability that X is positive is...
(Write the answer in the form of a fraction with 2 decimal places.)

Hello, anyone interested to practice this question to sharpen your probability skills? If you want, please post the steps and result. Thank you greatly.
I wish you a happy 2020 & 2021, too. )

Mai

 

[Deleted member 4993]

A variable X is a mixture of two normal variables: the first one has expectation 3 and standard deviation 1, the second one has expectation 1 and standard deviation 2. The mixture law is (0.5,0.5)
The probability that X is positive is...
(Write the answer in the form of a fraction with 2 decimal places.)

Hello, anyone interested to practice this question to sharpen your probability skills? If you want, please post the steps and result. Thank you greatly.
I wish you a happy 2020 & 2021, too. )

Mai

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