Download 7-3: Areas Under Any Normal Curve

3/21/2013
7-3: Areas Under Any Normal
Curve
To find areas and probabilities for a random variable x that
follows a normal distribution given mean and standard
deviation, convert x values to z values using the formula
x 
z

and use the table.
Calculator option:
• normalcdf(lower bound, upper bound, mean, standard
deviation)
Ex: Assume x has a normal distribution. Find the indicated
probabilities.
P(x  6);  4;  1
P(x  8);  15;  4.4
P(4  x  10);  5.5;  2
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Inverse Normal Distribution - used to find the x or z values
that correspond to a given area under the normal curve
• remember: x  z  
Calculator Option: invNorm(area to the left, mean,
standard deviation)
Ex: Texas Instruments wishes to guarantee their graphing
calculators for a certain number of years. The research
department has found that the mean life of a graphing
calculator is 11 years with a standard deviation of 3 years.
How long can the guarantee period be if management doesn’t
want to replace more than 4% of the calculators sold?
Ex: Find the z value described and sketch the area described.
a) Find z such that 4.8% of the standard normal curve lies to
the left of z.
b) Find z such that 77% of the standard normal curve lies to the
right of z.
c) Find z such that 90% of the standard normal curve lies
between -z and z.
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Ex: p. 278 #23
Ex: p. 278 #24
Assignment:
p. 277-280 #2-20 evens; 21-29 all
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