Probability help! (normal dist)

[barydos]

Hey all!

i'll just get to the point, I need help with the following question (well just part b)

The amount of a certain chemical in a type A cell is normally distributed with mean of 10 and a standard deviation of 1, while the amount in a type B cell is normally distributed with a mean of 14 and a standard deviation of 2. To determine whether a cell is a type A or a type B, the amount of chemical in the cell is measured and the cell is classified as a type A if the amount is less than a specified value c, and as being of type B otherwise.

a) If c=12 calculate the probability that a type A cell will be misclassified, and the probability that a type B cell will be misclassified.

b) Find the value of c for which the two probabilities of misclassification are equal.

Thanks in advance,

[BubbleWrapMan]

We have and

a) If A>12 then it will be misclassified, and if B<12 it will be misclassified, so you need to find and using CAS

b)

[barydos]

thank you, you're the best! :D:D:D