The negative value denotes that the labor cost of $75 was 0.681818 standard deviations lower than the average television repair cost of $90.
The z-score for the $100 labor cost
From the z-value, positive implies that the repair cost was above the mean cost by 0.454545 standard deviations.
Question 2
Part a
The shaded region in figure 1 represents the area between the mean and the z-score obtained.
Figure 1: Area Required
From the z-score table,
Therefore,
Part b
The area bounded by 395 pounds and the mean is shown in figure 2 below.
Figure 2: Area for 395 pounds
From the z-score table,
Thus,
Part c
From part b, the z-score corresponding to 395 pounds equals . The area corresponding to a value of 395 pounds or less is shaded blue in figure 3 below. Using a z-value table, the probability corresponding to the area equals 0.3085.
Figure 3: Area for 395 pounds or less
Question 3
Given that,
A 5% chance corresponds to a probability of .
Using the z-table,
Hence, the inventory level should be set at 1570.125 units.
Question 4
Part a
A 38% chance denotes to a probability of .
Applying the normal approximation,
Using a z-table, a
Hence,
Part b
Applying the normal approximation,
Using a z-table, a
Hence,
Part c
Applying the normal approximation,
Using a z-table, a
Hence,
Using a z-table, a
Hence,
Question 5
Part a
Expected number of disasters
Part b
Applying the normal approximation,
Using a z-table, a
Hence,
