Answer:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
Step-by-step explanation:
For this case we define our random variable X as "fat content per hot dog" and we know the following parameters:
[tex]\mu = 20, \sigma =1.9[/tex]
We select a sample of n=35 and we want to find the following probability:
[tex] P(\bar X>20.5)[/tex]
For this case since the sample size is >30 we can use the central limit theorem and we use the z score formula given by:
[tex]z=\frac{\bar X -\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
Replacing we got:
[tex]z=\frac{20.5-20}{\frac{1.9}{\sqrt{35}}}= 1.557[/tex]
And using the normal standard distribution and the complement rule we got:
[tex]P(z>1.557) =1-P(z<1.557) = 1-0.940 = 0.06[/tex]
