Answer :
Answer:
option d. 30%
Step-by-step explanation:
Data provided in the question:
[tex]a=0[/tex]
[tex]b=15[/tex]
Now,
The probability density function of the uniform distribution is given as:
[tex]f(x)=\frac{1}{15-0}[/tex]
[tex]f(x)=\frac{1}{15}, 0<x<15[/tex]
Therefore,
The required probability will be
[tex]P(X<4.5)=\int_{0}^{4.5} f(x) d x[/tex]
[tex]P(X<4.5)=\int_{0}^{4.5} \frac{1}{15} d x[/tex]
[tex]P(X<4.5)=\left(\frac{x}{15}\right)_{0}^{4.5}[/tex]
[tex]P(X<4.5)=\left(\frac{4.5}{15}-\frac{0}{15}\right)[/tex]
[tex]P(X<4.5)=0.3[/tex]
or
= 0.3 × 100%
= 30%
Hence,
The answer is option d. 30%