Question

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

distributed with mean μ = 854 grams and standard deviation of σ = 12 grams.

(e) Find the probability that a random sample of 30 jars has a mean weight

between 844 and 858 grams. (Give your answer correct to four decimal places.)

(with step by step please)

Answer 1

Solution :

Given that ,

mean =   = 854

standard deviation = =   12

n = 30

= 854

=  / n= 12 / 30=2.1909

P( 844<     <858 ) = P[( 844-854) /2.1909  < ( - ) /   < ( 858-854) /2.1909 )]

= P(-4 < Z < 1.83)

= P(Z < 1.83) - P(Z < -4)

Using z table

=0.9664-0

=0.9664

probability=0.9664