The number of minutes that Samantha waits to catch the bus is uniformly distributed between 0 and 15 minutes. What is the probability that Samantha has to wait less than 4.5 minutes to catch the bus?

a. 10%
b. 3%
c. 20%
d. 30%

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%

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