Question

taylors computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve. what percentage of numbers randomly generated by taylors computer are less than 0.5? 12.5% 25% 50% 87.5%

Explanation:

Step1: Calculate the base and height of the rectangle for numbers less than 0.5

The base is \(0.5 - 0=0.5\), and the height is \(\frac{1}{4}\).

Step2: Calculate the area of the rectangle (probability)

The area of a rectangle is \(A=\text{base}\times\text{height}\). So \(A = 0.5\times\frac{1}{4}=\frac{0.5}{4}=\frac{1}{8}\).

Step3: Convert the fraction to a percentage

To convert \(\frac{1}{8}\) to a percentage, use the formula \(\text{Percentage}=\frac{1}{8}\times100\%\). \(\frac{1}{8}\times100\% = 12.5\%\)

Answer:

12.5%