Advanced math question that has me stumped.
A set of data is normally distributed with a mean of 500 and a standard deviation of 40.
Find the probability that a value selected at random is less than 420.

Question

Advanced math question that has me stumped.
A set of data is normally distributed with a mean of 500 and a standard deviation of 40. 
Find the probability that a value selected at random is less than 420.

anonymous · Answer

I think that there is a 2.4% chance of that occurring but I could be very wrong and I am not sure how to get the probability from that.

anonymous · Answer

$$P(X<420)=P\left(\frac{X-500}{40}<\frac{420-500}{40}\right)=P(Z<-2)$$ Refer to a left-tail probability table: http://dsearls.org/courses/M120Concepts/ClassNotes/Statistics/520A_LeftTailTable.htm

anonymous · Answer

Looks like it's closer to 2.3%

anonymous · Answer

umm not to appear stupid or anything but that table... not quite sure what is what o_o

ganeshie8 · Answer

Also, 80 is 2 standard deviations away from the mean - So if you're not taught Ztables yet, you can simply use the thumb rule : http://en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule

ganeshie8 · Answer

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