The amount of fill (weight of contents) put into a glass jar of spaghetti sauce

Question

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean = 855 grams and standard deviation of = 11 grams.

(a) Describe the distribution of x, the amount of fill per jar.

skewed rightnormal     skewed leftchi-square

(b) Find the probability that one jar selected at random contains between 841 and 863 grams. (Give your answer correct to four decimal places.)

(c) Describe the distribution of x, the mean weight for a sample of 24 such jars of sauce.

skewed rightnormal     skewed leftchi-square

(d) Find the mean of the x distribution. (Give your answer correct to the nearest whole number.)


(ii) Find the standard error of the x distribution. (Give your answer correct to two decimal places.)


(e) Find the probability that a random sample of 24 jars has a mean weight between 841 and 863 grams. (Give your answer correct to four decimal places.)

Explanation / Answer

a) Normal distribution with Mu = 855 and sigma = 11
b) z = (X-Mu)/sigma
z1 = (841-855)/11 = -1.2727
z2 = (863-855)/11 = +0.7272
Required probability = P(841 < X < 863)
= P(-1.2727 < z <0.7272 )
= 0.53312               (By using STANDARD NORMAL DISTRIBUTION table and Z score)
c) Normal distribution
d) Mean = 855 and Standard error of mean = SEx = sigma/sqrt n = 11/sqrt 24 = 2.24536

e) z = (X-Mu)/SEx
z1 = (841-855)/2.24 = 6.25
z2 = (863-855)/2.24 =+3.5714
Required probability = P(841 < X < 863)
= P(6.25 < z < +3.5714)
= 1.0000 approximately (By using STANDARD NORMAL DISTRIBUTION table and Z score)

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