taylors computer randomly generate numbers between 0 and 4, as represented by the given uniform density…

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% random number generated by computer 1/4 0 1 2 3 4 random number

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% random number generated by computer 1/4 0 1 2 3 4 random number

Answer

Explanation:

Step1: Recall uniform - distribution formula

For a uniform distribution on the interval $[a,b]$, the probability density function is $f(x)=\frac{1}{b - a}$ for $a\leq x\leq b$ and $0$ otherwise. Here, $a = 0$ and $b = 4$, so $f(x)=\frac{1}{4}$ for $0\leq x\leq 4$.

Step2: Use the probability formula for uniform distribution

The probability $P(X\lt x)$ for a uniform distribution on $[a,b]$ is given by $P(X\lt x)=\frac{x - a}{b - a}$ when $a\leq x\leq b$. We want to find $P(X\lt0.5)$ with $a = 0$ and $b = 4$. Substitute into the formula: $P(X\lt0.5)=\frac{0.5-0}{4 - 0}$.

Step3: Calculate the probability

$P(X\lt0.5)=\frac{0.5}{4}=\frac{1}{8}=0.125$.

Step4: Convert to percentage

To convert the probability to a percentage, multiply by 100. So $0.125\times100 = 12.5%$.

Answer:

12.5%