Statistics help, please!?

Question

Find P(11 < x < 16) when mu = 15 and sigma = 3. Write your steps in probability notation.

Answer 1

20% statistics are made up 90% of the time!!  

Answer 2

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 distribution 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.

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( μ = 15 , σ² = 9 )

X ~ Normal( μ = 15 , σ = 3 )

Find P( 11 &lt; X &lt; 16 )

= P( ( 11 - 15 ) / 3 &lt; ( X - μ ) / σ &lt; ( 16 - 15 ) / 3 )

= P( -1.333333 &lt; Z &lt; 0.3333333 )

= P( Z &lt; 0.3333333 ) - P( Z &lt; -1.333333 )

= 0.6305587 - 0.09121122

= 0.5393474  

Answer 3

P(11 &lt; x &lt; 16)

=  P(11 &lt; x &lt; 15) + P(15 &lt; x &lt; 16)  

=P((11-15)/3 &lt; x &lt; (15-15)/3) + P((15-15)/3 &lt; x &lt; (16-15)/3)

=P(-1.333 &lt; x &lt; 0) + P(0 &lt; x &lt; 0.333)

=P(0&lt; x &lt;1.333) + P(0 &lt; x &lt; 0.333)