Question

taylor’s computer randomly generate numbers between 0 and 4, as represented by the given uniform density curve. random number generated by computer what percentage of numbers randomly generated by taylor’s computer is greater than 1.9? 25% 47.5% 52.5% 75%

Explanation:

Step1: Identify the distribution

This is a uniform distribution between \( a = 0 \) and \( b = 4 \). The probability density function (pdf) for a uniform distribution is \( f(x)=\frac{1}{b - a} \) for \( a\leq x\leq b \), and 0 otherwise. Here, \( f(x)=\frac{1}{4-0}=\frac{1}{4} \) for \( 0\leq x\leq 4 \).

Step2: Calculate the probability \( P(X > 1.9) \)

For a uniform distribution, the probability that \( X \) is greater than a value \( c \) (where \( a\leq c\leq b \)) is given by the area of the rectangle to the right of \( c \). The length of the interval to the right of \( 1.9 \) is \( b - c=4 - 1.9 = 2.1 \). The height of the pdf is \( \frac{1}{4} \), but since we are dealing with probability (which is the area, length × height), and the height is \( \frac{1}{4} \), the probability \( P(X > 1.9)=(b - c)\times f(x)=(4 - 1.9)\times\frac{1}{4} \).

First, calculate \( 4 - 1.9 = 2.1 \). Then, \( 2.1\times\frac{1}{4}=0.525 \). To convert this to a percentage, multiply by 100: \( 0.525\times100 = 52.5\% \).

Answer:

52.5% (corresponding to the option "52.5%")