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liluv5062
02.03.2020 •
Mathematics
A perfume bottle is designed to have a capacity of 15 ounces. There is variation in the bottle manufacturing process. Based on historical data, let’s suppose that the bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2 ounces. What proportion of these bottles will have a capacity between 14.4 and 15.6 ounces?
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Ответ:
0.9974 proportion of these bottles will have a capacity between 14.4 and 15.6 ounces
Step-by-step explanation:
The bottle capacity can be reasonably modeled by a normal distribution with a mean of 15 ounces and a standard deviation of 0.2 ounces.
Mean = 15 ounces
Standard deviation = 0.2 ounces
We are supposed to find proportion of these bottles will have a capacity between 14.4 and 15.6 ounces i.e.P(14.4<x<15.6)
At x = 15.6
z=3
P(z<3)=0.9987
At x = 14.4
z=-3
P(z<-3)=.0013
P(14.4<x<15.6)=P(-3<z<3)=P(z<3)-P(z<-3)=0.9987-0.0013=0.9974
Hence 0.9974 proportion of these bottles will have a capacity between 14.4 and 15.6 ounces
Ответ:
im pretty sure its
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