Answer: 97.72%
Step-by-step explanation:
Given : A shoe manufacturer collected data regarding men's shoe sizes and found that the distribution of sizes exactly fits the normal curve.
Let x be the random variable that represents the shoe sizees.
Also, The population mean = [tex]\mu=11[/tex] ; Standard deviation: [tex]\sigma=1.5[/tex]
Formula for z:-
[tex]z=\dfrac{x-\mu}{\sigma}[/tex]
Put x= 8, we get
[tex]z=\dfrac{8-11}{1.5}=-2[/tex]
Now, the probability that the male shoe sizes are greater than 8 :-
[tex]P(x>8)=P(z>-2)=1-P(z\leq-2)\\\\=1-0.0227501=0.9772499\approx0.9772[/tex]
Hence, the percent of male shoe sizes are greater than 8 is 97.72%.
