Question

2) A brand of salsa comes in jars narked net veight 680 grams. Supposs mean net veight is μ = 680 g with a standard deviation of the actual σ. 22.79. Pur ther suppose that the net veights are normally distributed. a) Determine the probability that a randomly selected jar of this brand of salsa vill have a veight less t 660 g. brand of salsa vill have a mean veight less than 660 9: eeb Na ar 0003 aoo 3 3.-41 alpes 又ごし40 40.5 5 et He brcaLs (ato,02

Answer 1

Given,

$\mu$ = 680 ,$\sigma$ = 22.7

We convert this to standard normal as

P( X < x) = P( Z < x -  $\mu$ / $\sigma$)

a)

P( X < 660) = P( Z < 660 - 680 / 22.7)

= P( Z < -0.88)

= 1 - P( Z < 0.88)

= 1 - 0.8106

= 0.1894

b)

Using central limit theorem,

P($\bar{x}$ < x) = P( Z < x -  $\mu$ / ( $\sigma$ / sqrt( n) ) )

P( $\bar{x}$ < 660) = P( Z < 660 - 680 / ( 22.7 / sqrt(15) ))

= P( Z < -3.41)

= 1 - P( Z < 3.41)

= 1 - 0.9997

= 0.0003