Question

Taylor's computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve.

Answer 1

12.5% is the percentage of numbers randomly generated by Taylor's computer that is less than 0.5.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

The percentage of numbers randomly generated by Taylor's computer are less than 0.5 is given by

P(0≤X≤0.5)

=$\int_{0}^{0.5}\frac{1}{4}dx$

$=\frac{1}{4}x|^{0.5}_{0}$

$=\frac{1}{4}(0.5-0)$

$=0.25(0.5)$

= 0.125

That is 12.5%

Learn more about density curves here-

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