Question

data collected from a coffee shop indicate that the price of a drink forms a consistent pattern that can be graphed as the given uniform density curve. what proportion of drinks cost less than $5.50? 0.083 0.167 0.417 0.833

Explanation:

Step1: Determine the base and height of the rectangle

The base of the rectangle for the interval we want (from \(x = 3\) to \(x=5.5\)) is \(b=5.5 - 3=2.5\). The height \(h\) of the uniform density curve is \(\frac{1}{3}\) (since the total interval is from \(x = 3\) to \(x = 6\), length \(L=6 - 3 = 3\), and for a uniform distribution \(h=\frac{1}{L}\)).

Step2: Calculate the area of the rectangle

The area \(A\) of a rectangle is \(A=b\times h\). Substitute \(b = 2.5\) and \(h=\frac{1}{3}\) into the formula: \(A=2.5\times\frac{1}{3}=\frac{2.5}{3}=\frac{25}{30}=\frac{5}{6}\approx0.833\).

Answer:

\(0.833\)