Question

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean μ = 843 grams and standard deviation of σ = 8 grams.

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

1) skewed right

2) normal    

3) skewed left

4) chi-square

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(b) Find the probability that one jar selected at random contains between 835 and 865 grams. (Give your answer correct to four decimal places.)

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(c) Describe the distribution of x, the mean weight for a sample of 20 such jars of sauce.

1) skewed right

2) normal

3) skewed left

4) chi-square

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(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 20 jars has a mean weight between 835 and 865 grams. (Give your answer correct to four decimal places.)

Answer 1

olution :

Given that,

mean = = 843

standard deviation = = 8

A ) The distribution of x, the amount of fill per jar.

Option normal is correct.

B ) P ( 835 < x < 865 )

P ( 835 - 843 / 8) < ( x -  / ) < ( 865 - 843 / 8)

P ( - 8 / 8 < z < 22/ 8 )

P (- 1 < z <2.75 )

P (z < 2.75 ) - p ( z < - 1 )

Using z table

= 0.9970 - 0.1587

= 0.8383

Probability = 0.8383

C ) The distribution of x, the mean weight for a sample of 20 such jars of sauce.

Option normal is correct.

D ) n = 20

The mean of the x distribution.

= 843

The standard error of the x distribution.

   =  ( /n) = (8 / 20 ) = 1.79

E ) P ( 835 < < 865 )

P ( 835 - 843 / 1.79) < ( -  / ) < ( 865 - 843 / 1.79)

P ( - 8 / 1.79 < z < 22/ 1.79 )

P (- 4.47 < z < 12.29)

P (z < 12.29 ) - p ( z < - 4.47 )

Using z table

= 1 - 0

= 1.0000

Probability = 1.0000