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 between 11.9 ounces and 12.1 ounces. Find the probability if the sample is just 1 cup.

Answer 1

Solution :

Given that,

mean = = 12

standard deviation = = 0.2

a) n = 9

=   = 12

= / n = 0.2/ 9 = 0.0667

P(11.9 < < 12.1)  

= P[(11.9 - 12) /0.0667 < ( - ) / < (12.1 - 12) / 0.0667)]

= P(-1.5 < Z < 1.5)

= P(Z < 1.5) - P(Z < -1.5)

Using z table,  

= 0.9332 - 0.0668  

= 0.8664

b) P( 11.9 < x < 12.1) = P[(11.9 - 12)/ 0.2) < (x - ) /  < (12.1 - 12) / 0.2) ]

= P( -0.5 < z < 0.5)

= P(z < 0.5) - P(z < -0.5)

Using z table,

= 0.6915 - 0.3085

= 0.3830