Please help me understand this is asking and how to solve.

Question

P(-2>Z and Z<-1)=
and
X~N(3,4). Find value c such that P(c<x)=.7
Thank You!

Answer 1

P(-2>Z and Z<-1)
or more commonly written as
P(-2 > Z <-1)
wants you to find the probability that the z-score of the normal binomial distribution lies between
-2 and -1

X~N(3,4) or X~N(3,2^2)
means X is normally distributed with a mean of 3 and a standard deviation of 2

These are common notations you should find in your text or in your class notes.

You must have been supplied with tables of the normal distribution.
If not you will find this applet extremely useful.

http://davidmlane.com/normal.html

Answer 2

What is the probability that the average lifetime of 25 bulbs would be no more than 1550 given mean of 1500 and standard deviation of 200 hours.
I know that it is asking P(x less than or equal to 1550), x is 25, u equal 1500 and sd is 200. I'm having problems getting to the final answer.
Thank YOu!

Answer 3

I will assume that you are working from "tables", so we need the z-score for 1550

z-score = (1550 - 1500)/200 = .25

look at
http://math.arizona.edu/~rsims/ma464/standardnormaltable.pdf
and find .25
(2nd page , find .2 in 1st column, then under .05)
to find .59871
which is the probability of your event.

The beauty of
http://davidmlane.com/normal.html
is that we don't even have to bother with z-scores.
just enter the mean of 1500
the sd of 200
click on the "below" button after entering 1550
to get .5987