a vending machine dispenses coffee into an eight -ounce cup. The amount of coffee dispensed
into the cup is normally distributed with sd 0.02 ounce . you can allow the cup to overfill
5% of the time .What amount should you set a mean amount of coffee to be dispensed ?
please
To determine the mean amount of coffee that should be dispensed, we need to find the value that corresponds to the 95th percentile of the normally distributed data.
Step 1: Calculate the z-score associated with the 95th percentile.
The z-score represents how many standard deviations away from the mean a particular value is located. We can use a standard normal distribution table or a statistical calculator to find the z-score associated with the 95th percentile. In this case, the 95th percentile corresponds to a z-score of approximately 1.645.
Step 2: Use the z-score formula to find the mean amount.
The formula to calculate the mean amount is: Mean = μ + (z * standard deviation)
Given:
Standard deviation (σ) = 0.02 ounce
95th percentile z-score (z) = 1.645
Mean = μ + (1.645 * 0.02)
Step 3: Calculate the mean amount.
Now, substitute the values into the formula and solve for the mean amount.
Mean = μ + (1.645 * 0.02)
Mean = μ + 0.0329
Therefore, the mean amount of coffee you should set to be dispensed is equal to the desired cup size minus the value obtained from the calculation. In this case, the mean amount of coffee dispensed should be:
8 - 0.0329 = 7.9671 ounces