Suppose that the actual amount of instant coffee X that a fi

Suppose that the actual amount of instant coffee (X) that a filling machine puts into “6-ounce” jars is a random variable having a normal distribution with = 0.05 ounce. If only 3 percent of the jars are to contain less than 6 ounces of coffee, what must be the mean fill of these jars? Using the derived mean, find the P(X > 6.1). a) Show all your work. * You can use normal tables or technology to find the required answers. Make sure you mention what you have used. (Example – I used TI-84 normalcdf(lowerbd, upperbd, mu, sigma))

Solution

Normal Distribution
Mean ( u ) =6
Standard Deviation ( sd )=0.05
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X > 6.1) = (6.1-6)/0.05
= 0.1/0.05 = 2
= P ( Z >2) From Standard Normal Table
= 0.0228