Answer:
The probability that between 64 and 90 of them read the ingredients listed on a product's label is 0.82.
Step-by-step explanation:
We know the proportion of the population, that is π=0.28.
The standard deviation for this sampling distribution is
[tex]\sigma=\sqrt{\frac{\pi(1-\pi)}{N} } =\sqrt{\frac{0.28*0.72}{256} }= 0.028[/tex]
The value 64 represents a proportion of p=64/256=0.25, and the value 90 represents p=90/256=0.35.
With these values, we can calculate the z-values.
[tex]z_1=\frac{p_1-\pi}{\sigma} =\frac{0.25-0.28}{0.028} =\frac{-0.03}{0.028} =-1.07\\\\z_2=\frac{p_2-\pi}{\sigma} =\frac{0.35-0.28}{0.028} =\frac{0.07}{0.028} =2.5[/tex]
The probability that between 64 and 90 read the ingredients is:
[tex]P=P(64<x<90)=P(-1.07<z<2.50)=P(z<2.50)-P(z<-1.07)\\\\P=0.99379-0.14231=0.82148[/tex]
The probability that between 64 and 90 of them read the ingredients listed on a product's label is 0.82.
