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11.04.2020 •
Mathematics
A set of magical wand prices are normally distributed with a mean of 50 dollars and a standard deviation of 4 dollars. A blackthor wand has a price of 45.20 dollars. What proportion of wand prices are lower than the price of the blackthorn wand? You may round your answer to four decimal places.
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Ответ:
The proporion of wand prices lower then the blackthron wand is 0.1151
Step-by-step explanation:
Normal Distribution
Also known as the Bell Curve by its characteristic shape where most values are concentrated in the center of the curve and they are rapidly spread out through both tails.
The parameters needed to compute probabilities with the normal distribution are: the mean
and the standard deviation
. The curve is often called as N(
,
).
The values of the probabilities are usually given in tables or computed by digital means like Excel or any online calculator. We'll use the Excel Normal Distribution formula
NORM.DIST(x,mean,standard_dev,cumulative)
This formula gives the left tail of the curve, i.e. P(x<X). The values provided in the problem are
The formula will be applied like this
NORM.DIST(45.20,50,4,TRUE)
It gives the value
P(x<45.20)=0.1151
The proporion of wand prices lower then the blackthron wand is 0.1151
Ответ: