If #X# is normally distributed, how do I find #"P"(X<5.83)#?
1 Answer
Find the corresponding
Explanation:
If the question is asking you to use the standard normal distribution
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Look up 5.83 in a
#z# -table. Unfortunately, no#z# -table in wide publication will list values higher than 3.5, because at that point, the value they give is within 0.01% of 100%. Higher#z# -values than 3.5 are hardly practical. -
Use computer software (or a web utility) to find out what percentage of the standard normal distribution is to the left of
#x=5.83# . Using R, I found that the area under the curve to the left of#x=5.83# is approximately 0.99999999722863. In other words, ridiculously close to 1.
This leads me to think that perhaps the question is using a non-standard normal distribution. If that is the case, you can still calculate
#z=(x-mu)/sigma#
Subtracting
#P(X<5.83)=P(Z<(5.83-mu)/sigma)#
#color(white)(P(X<5.83))=P(Z<(5.83-3)/2)#
#color(white)(P(X<5.83))=P(Z<2.83/2)#
#color(white)(P(X<5.83))=P(Z<1.415)# .
This