Answer:
The probability that on a given day below 6,214,323 drinks are sold is 0.8413.
Step-by-step explanation:
The provided information are:
Population mean
= 6,205,195
Population standard deviation
= 9,120.32
Consider, <em>X</em> be the random variable that represents the number of drinks that are sold on a given that is normally distributed with the mean = 6,205,195 and standard deviation = 9,120.32.
The probability that on a given day below 6,214,323 drinks are sold can be calculated as:
![P(X](https://tex.z-dn.net/?f=P%28X%3C6%2C214%2C323%29%20%3D%20P%28%5Cfrac%7BX-%5Cmu%7D%7B%5Csigma%7D%20%3C%20%5Cfrac%7B6%2C214%2C323-%5Cmu%7D%7B%5Csigma%7D%20%29%5C%5CP%28X%3C6%2C214%2C323%29%20%3D%20P%28Z%20%3C%20%5Cfrac%7B6%2C214%2C323-6205195%7D%7B9120.32%7D%20%29%5C%5CP%28X%3C6%2C214%2C323%29%20%3D%20P%28%20Z%20%3C%201.0008%29%5C%5CP%28X%3C6%2C214%2C323%29%20%3D%200.8413)
It must be noted that <em>P</em>(<em>Z</em> < 1.0008) = 0.8413 has been calculated using the standard normal table.
Hence, the required probability is 0.8413.