Answer:
The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099
Step-by-step explanation:
A set of electric toothbrush prices are normally distributed with a mean of 87 dollars and a standard deviation of 8 dollars.
[tex]Mean = \mu = 87[/tex]
Standard deviation = [tex]\sigma = 8[/tex]
We are supposed to find proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars i.e.P(104.60<x<108.20)
[tex]Z=\frac{x-\mu}{\sigma}[/tex]
At x = 104.60
[tex]Z=\frac{104.60-87}{8}[/tex]
Z= 2.2
At x=108.20
[tex]Z=\frac{108.20-87}{8}[/tex]
Z= 2.65
Refer the z table for p value :
P(x<108.20)-P(x<104.60)=P(Z<2.65)-P(Z<2.2)=0.9960-0.9861=0.0099
Hence The proportion of electric toothbrush prices are between 104.60 dollars and 108.20 dollars is 0.0099
