Question

records show that oliver is typically 10 - 30 minutes late for his shift at work. the distribution for the minutes he is late forms a consistent pattern, which can be graphed as the given uniform density curve. oliver will get a written warning if he is more than 16 minutes late for work. what percentage of the time will oliver get a written warning? 30% 46.7% 70% 100%

Explanation:

Step1: Calculate the length of the total interval

The total interval for being late is from \(10\) to \(30\) minutes. The length of the total interval \(a = 30 - 10=20\) minutes.

Step2: Calculate the length of the interval for getting a warning

The interval for getting a warning is from \(16\) to \(30\) minutes. The length of this interval \(b = 30 - 16 = 14\) minutes.

Step3: Calculate the percentage using the formula for uniform distribution

The probability (percentage) in a uniform distribution is given by \(P=\frac{\text{length of relevant interval}}{\text{length of total interval}}\). So \(P=\frac{14}{20}\times100\% = 70\%\)

Answer:

70%