Answer:
2.5
Step-by-step explanation:
We are given that
Mean=[tex]\mu=3.2[/tex] pounds
Standard deviation=[tex]\sigma=0.8[/tex] pounds
n=25
We have to find the Z-score if the mean of a sample of 25 roasts is 3.6 pounds.
We know that Z-score formula
[tex]Z=\frac{\bar X-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]
We have [tex]\bar X=3.6[/tex]
Substitute the values then we get
Z- score=[tex]\frac{3.6-3.2}{\frac{0.8}{\sqrt{25}}}[/tex]
Z- score=[tex]\frac{0.4}{\frac{0.8}{5}}=\frac{0.4\times 5}{0.8}=2.5[/tex]
Hence, the Z-score value for the given sample mean=2.5
