Question

A manufacturing process produces bags of cookies that have Normally distributed weights with a mean of μ = 15.5 oz. and a standard deviation of σ = 0.4 oz. What is the probability that a randomly selected bag weighs more than 15.2 oz? What is the probability that 16 randomly selected bags have a mean weight that exceeds 15.2 oz?

Answer 1

Solution :

Given ,

mean = = 15.5

standard deviation = = 0.4

P(x >15.2 ) = 1 - P(x< 15.2)

= 1 - P[(x -) / < (15.2-15.5 ) /0.4 ]

= 1 - P(z < -0.75)

Using z table

= 1 - 0.2266

= 0.7734

probability= 0.7734

b.

n = 16

=   15.5

= / n = 0.4 / 16 = 0.1

P( >15.2 ) = 1 - P( <15.2 )

= 1 - P[( - ) / < (15.2-15.5) / 0.1]

= 1 - P(z < -3)

Using z table

= 1 - 0.0013

probability=0.9987

=

probability=