Question

The amount of fill (weight of contents) put into a glass jar of spaghetti sauce is normally distributed with mean μ = 859 grams and standard deviation of σ = 15 grams.

b) Find the probability that one jar selected at random contains between 841 and 860 grams. (Give your answer correct to four decimal places.)

(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 841 and 860 grams. (Give your answer correct to four decimal places.)

Answer 1

Solution :

Given that ,

mean = = 859

standard deviation = = 15

a) P( 841 < x < 860 ) = P[(841 - 859)/ 15 ) < (x - ) /  < (860 - 859) / 15 ) ]

= P(-1.20 < z < 0.07)

= P(z < 0.07) - P(z < -1.20)

Using z table,

= 0.5279 - 0.1151

= 0.4128

b) n = 20

= = 859

= / n = 15 / 20 = 3.35

e) P(841 < < 860)  

= P[(841 - 859) /3.35 < ( - ) / < (860 - 859) / 3.35)]

= P(-5.37 < Z < 0.30)

= P(Z < 0.30) - P(Z < -5.37)

Using z table,  

= 0.6179 - 0  

= 0.6179