Question

An on-the-job injury occurs once every 10 days on
average at an automobile plant. What is the probability that
the next on-the-job injury will occur within

a. 10 days?

b. 5 days?

c. 1 day?

Answer 1

The probability that the next on-the-job injury will occur within 10, 5, and 1 day are 0.632, 0.393, and 0.095

What is probability?

It is defined as the ratio of the number of favourable outcomes to the total number of outcomes, in other words, the probability is the number that shows the happening of the event.

We know the exponential distribution is given by;

$\rm P(X < t)=1-e^{-\dfrac{1}{\mu}t}$

The probability that the next on-the-job injury will occur within 10 days:

$\rm P(X < 10)=1-e^{-\dfrac{1}{10}10}$

P(X< 10) = 0.632

The probability that the next on-the-job injury will occur within 20 days:

$\rm P(X < 5)=1-e^{-\dfrac{1}{10}5}$

P(X< 5) = 0.393

The probability that the next on-the-job injury will occur within 1 days:

$\rm P(X < 1)=1-e^{-\dfrac{1}{10}1}$

P(X< 1) = 0.095

Thus, the probability that the next on-the-job injury will occur within 10, 5, and 1 day are 0.632, 0.393, and 0.095

Learn more about the probability here:

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