Question

19.The retail price of 1 pound roast ground coffee has a skewed distribution with a mean 4.78 dollars and a standard deviation of 0.61 dollars. A sample random sample of 36 bags of 1 pound roast ground coffee is chosen. Let represent the mean retail price of 36 bags of 1 pound roast ground coffee. (1)(2.5 points) We know the sampling distribution of the sample mean has approximately a normal distribution because of (a)the Law of Large Numbers. (b)the Central Limit Theorem. (c)the population we’re sampling from has a Normal distribution. (d)the Empirical Rule (2)(1.5 points) Compute the mean and standard deviation of the sampling distribution of . (3)(2.5 points) Compute and interpret the z-score for = 4.90. (4)(2.5 points) Compute (5)(3.5 points) Is it unusual that ? Explain why or why not. (you need show your work)

Answer 1

so the mean of sampling distribution of sample mean is 4.78 and stand deviation is 0.1017 .

Now Z score for any x =  

For X = 4.90 ,

Z score = = 0.1089

That indicates the sample mean 4.9 is 0.1089 standard deviation above from the mean .

This z score is not unusual . Because any value is said to be unusual if the Z Score is less than -2 or more than 2 . But here Z score is very close to 0 . Which indicates that 4.9 is very usual and close to the mean value .