A random sample of size 6 is selected from a normal distribution with mean 10 and variance 2. Calculate the probability that 2 of the sample values are less than 9, and the remaining 4 sample values are less than 9.

I'm skeptical of the and they gave.

I said Pr(X<9) U Pr(X>9) .

therefore, Pr(X<9) +Pr(X>9)=0( empty set)

hence 2Pr(X<9) +4Pr(X>9)

Why is my reasoning wrong?

I have a problem similar to the above.

A variable X is distributed normally with mean 10 and standard deviation 2.

If three values of X are taken at random,calculate the probability that two of them are less than 12 and the other is greater than 12.

The ans to this problem says 14.74; 0.337 ?

I'm skeptical of the and they gave.

I said Pr(X<9) U Pr(X>9) .

therefore, Pr(X<9) +Pr(X>9)=0( empty set)

hence 2Pr(X<9) +4Pr(X>9)

Why is my reasoning wrong?

I have a problem similar to the above.

A variable X is distributed normally with mean 10 and standard deviation 2.

If three values of X are taken at random,calculate the probability that two of them are less than 12 and the other is greater than 12.

The ans to this problem says 14.74; 0.337 ?

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