Question

The company manufactures chocolate bars with nominal weight of 115 g per bar. In order to to avoid risk of short changing, the mean weight is set as 117 g and SD of 2 g.

What is the probability that :

(a) a random chocolate bar weighs between 116 gram and 120 gram?

(b) a particular sample mean would be less than 116.5 millimeters chosen of 40 random samples of chocolate bar.

Answer 1

Solution :

Given that ,

mean = = 117

standard deviation = = 2

a) P( 116 < x < 120) = P[(116 - 117)/ 2) < (x - ) /  < (120 - 117) / 2) ]

= P(-0.50 < z < 1.50)

= P(z < 1.50 ) - P(z < -0.50)

Using z table,

= 0.9332 - 0.3085

= 0.6247

b) = 117

= / n = 2 / 40 = 0.316

P( < 116.5) = P(( - ) / < (116.5 - 117) / 0.316)

= P(z < -1.58)

Using z table

= 0.0571