Help with Statistics question please?

Question

For the standard normal curve, compute the following probabilities:

a) P[ 0 < Z < 3]=

I got normalcdf(0,3,0,1)=.4987

b) P[-1.57 < Z ≤ .78]

not sure about this one

c)P[Z ≥ 1]=

I got normalcdf(-x,1,0,1)=.8413

d)P[Z < 1.45]=

I got normalcdf(-x,1.45,0,1)=.9265

Answer 1

You are correct.  in the one you didn&#039;t get you need only to enter the following into your calculator:

normalcdf( -1.57, 0.78, 0, 1)

For any normal random variable X with mean μ and standard deviation  ÃÂƒ , X ~ Normal( μ ,  ÃÂƒ ), (note that in most textbooks and literature the notation is with the variance, i.e., X ~ Normal( μ ,  ÃÂƒÃ‚² ).  Most software denotes the normal with just the standard deviation.)

You can translate into standard normal units by:

Z = ( X - μ ) /  ÃÂƒ

Moving from the standard normal back to the original distribuiton using:

X = μ + Z * σ

Where Z ~ Normal( μ  = 0,  ÃÂƒ  = 1).  You can then use the standard normal cdf tables to get probabilities.

If you are looking at the mean of a sample, then remember that for any sample with a large enough sample size the mean will be normally distributed.  This is called the Central Limit Theorem.

If a sample of size is is drawn from a population with mean μ and standard deviation σ then the sample average xBar is normally distributed

with mean μ and standard deviation  ÃÂƒ /√(n)

An applet for finding the values

http://www-stat.stanford.edu/~naras/jsm/...

calculator

http://stattrek.com/Tables/normal.aspx

how to read the tables

http://rlbroderson.tripod.com/statistics...

In this question we have

X ~ Normal( μx = 0 , σx² = 1 )

X ~ Normal( μx = 0 , σx = 1 )

P( 0 &lt; Z &lt; 3 )

= P( Z &lt; 3 ) - P( Z &lt; 0 )

= 0.9986501 - 0.5

= 0.4986501

P( -1.57 &lt; Z &lt; 0.78 )

= P( Z &lt; 0.78 ) - P( Z &lt; -1.57 )

= 0.7823046 - 0.05820756

= 0.724097

P( Z &gt; 1 )

= P( Z &lt; -1 )

= 0.1586553

P( Z &lt; 1.45 )

= 0.9264707