Final answer:
To determine how many trays of doughnuts the bakery should prepare each day to meet a service level of at least 95%, the owner can use the normal distribution and calculate the z-score corresponding to the desired service level. The z-score can then be used to determine the number of trays to be prepared.
Step-by-step explanation:
To determine how many trays of doughnuts the bakery should prepare each day, the owner can use the concept of service levels. The service level represents the probability of meeting or exceeding the demand. In this case, the owner wants a service level of at least 95%. Using the normal distribution, the owner can calculate the z-score corresponding to a service level of 0.95. A z-score of 1.645 corresponds to a service level of 0.95, and it represents the number of standard deviations above the mean that will satisfy the desired service level.
Next, the owner can use the z-score formula to calculate the number of trays that should be prepared:
Z = (X - mean) / standard deviation
where Z is the z-score, X is the number of trays to be prepared, mean is the mean demand (5 trays), and standard deviation is the standard deviation of demand (1 tray).
Substituting the values into the formula:
1.645 = (X - 5) / 1
Solving for X, we get:
X = 6.645
Rounding to the nearest whole tray, the owner should prepare 7 trays each day to meet the desired service level of at least 95%.