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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%

Answers

Answer 1
Answer:

Answer:

option d. 30%

Step-by-step explanation:

Data provided in the question:

a=0

b=15

Now,

The probability density function of the uniform distribution is given as:

f(x)=(1)/(15-0)

f(x)=(1)/(15), 0<x<15

Therefore,

The required probability will be

P(X<4.5)=\int_(0)^(4.5) f(x) d x

P(X<4.5)=\int_(0)^(4.5) (1)/(15) d x

P(X<4.5)=\left((x)/(15)\right)_(0)^(4.5)

P(X<4.5)=\left((4.5)/(15)-(0)/(15)\right)

P(X<4.5)=0.3

or

= 0.3 × 100%

= 30%

Hence,

The answer is option d. 30%
Answer 2
Answer:

Final answer:

In a uniform distribution, all values have an equal chance of occurring. To find the probability of Samantha waiting less than 4.5 minutes, you divide 4.5 by the total time interval of 15 minutes. The answer is 30%.

Explanation:

The question is about the concept of uniform distribution in probability, which means that each value within the given range has an equal chance of being drawn. In this case, Samantha can wait anywhere between 0 and 15 minutes, so each minute has an equally likely chance of being the waiting time. To find the probability that Samantha has to wait less than 4.5 minutes, we simply divide this time interval by the total time interval. Hence, the calculation is 4.5 / 15 = 0.30 or 30%. So, the answer to the question of the probability that Samantha has to wait less than 4.5 minutes to catch the bus is 30%.

Learn more about Uniform Distribution here:

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