Answer:
The probability that the sample mean weight of these 400 bags exceeded 10.6 ounces is P(Xs>10.6)=0.
Step-by-step explanation:
When we take samples of size n=400, we have the folllowing parameters for the sampling distribution for the sample means:
[tex]\mu_s=\mu=10.5\\\\ \sigma_s=\dfrac{\sigma}{\sqrt{n}}=\dfrac{0.1}{\sqrt{400}}=\dfrac{0.1}{20}=0.005[/tex]
We can calculate the probability that the sample mean weight of these 400 bags exceeded 10.6 ounces calculating the z-score for Xs=10.6 and then its probability P(Xx>10.6), using the standard normal distribution:
[tex]z=\dfrac{X_s-\mu_s}{\sigma_s}=\dfrac{10.6-10.5}{0.005}=\dfrac{0.1}{0.005}=20\\\\\\P(X_s>10.6)=P(z>20)=0[/tex]
