The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean ì = 843 grams and standard deviation of ó = 9 grams
(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)
843 Was my answer.
(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)
Not sure of formula to work this one
(e) Find the probability that a random sample of 20 jars has a mean weight between 836 and 855 grams. (Give your answer correct to four decimal places.)
Not sure of formula to work this one
2) SEm = SD/√n
e) Z = (score-mean)/SEm
Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.
To find the mean of the x distribution, in this case, you've correctly stated that the mean of the fill is 843 grams. Therefore, the mean of the x distribution is also 843 grams.
To find the standard error of the x distribution (SE), you can use the formula:
SE = σ /√n
where σ represents the standard deviation of the fill (9 grams in this case), and n represents the sample size. In this case, the sample size is 20 jars. Plugging in these values into the formula, we have:
SE = 9 / √20
Calculating this, we get:
SE ≈ 2.01 grams (rounded to two decimal places)
Now, to find the probability that a random sample of 20 jars has a mean weight between 836 and 855 grams, we can use the z-score formula to convert it into a standard normal distribution problem. The formula is:
z = (x - μ) / (σ / √n)
where x represents the desired mean weight range, μ represents the population mean (843 grams), σ represents the standard deviation (9 grams), and n represents the sample size (20 jars).
For the lower bound, the z-score is:
z1 = (836 - 843) / (9 / √20)
And for the upper bound, the z-score is:
z2 = (855 - 843) / (9 / √20)
Once you have these z-scores, you can use a standard normal distribution table or a calculator to find the respective probabilities. Subtracting the smaller probability (z1) from the larger probability (z2) will give you the desired probability of the mean weight falling between 836 and 855 grams.