Question is given as follow: The pH levels of food items prepared in a certain way are normally distributed with a standard deviation of 0.82. An experimenter estimates the mean pH level by averaging the pH levels of a random sample of n items.
If n = 5, what is the probability that the experimenter’s estimate is within 0.5 of the true mean value?
HINT:$$Pr(|\bar{X}-\mu|<0.5)$$ $$=Pr\left(\dfrac{|\bar{X}-\mu|}{\sigma /\sqrt{n}}<\dfrac{0.5}{\sigma/\sqrt{n}}=1.36\right)$$ $$=Pr\left(-1.36<\dfrac{\bar{X}-\mu}{\sigma /\sqrt{n}}<1.36\right)$$ where $Z=\dfrac{\bar{X}-\mu}{\sigma /\sqrt{n}}$ is standard normally distributed