Question

A coffee machine dispenses normally distributed amounts of coffee with a mean of 12 ounces and a standard deviation of 0.2 ounce. If a sample of 9 cups is selected, find the probability that the mean of the sample will be greater than 12.1 ounces. Find the probability if the sample is just 1 cup.

Answer 1

Solution :

Given that,

mean = = 12

standard deviation = = 0.2

n=9

= =12

= / n = 0.2/ 9 = 0.067

P( > 12.1) = 1 - P( < 12.1)

= 1 - P[( - ) / < (12.1-12) /0.067 ]

= 1 - P(z <1.49 )

Using z table

= 1 - 0.9319

= 0.0681

probability= 0.0681

b.

=0.2/ 1=0.2

P( > 12.1) = 1 - P( < 12.1)

= 1 - P[( - ) / < (12.1-12) /0.2 ]

= 1 - P(z <0.5 )

Using z table

= 1 - 0.6915

= 0.3085

probability= 0.3085