The number of failures of a testing instrument from contamination particles on the product is a poisson random variable with a mean of 0.018 failures per hour. (a) what is the probability that the instrument does not fail in an 8-hour shift? (b) what is the probability of at least 1 failure in a 24-hour day? round your answers to four decimal places (e. g. 98.7654).

The probability that the instrument does not fail in an 8-hour shift is

The probability of at least 1 failure in a 24-hour day is

Step-by-step explanation:

The probability distribution of a Poisson random variable X representing the number of successes occurring in a given time interval or a specified region of space is given by the formula:

Let X be the number of failures of a testing instrument.

We know that the mean failures per hour.

(a) To find the probability that the instrument does not fail in an 8-hour shift, you need to:

For an 8-hour shift, the mean is

(b) To find the probability of at least 1 failure in a 24-hour day, you need to:

For a 24-hour day, the mean is

b

step-by-step explanation:

the word superfluous means unnecessary

b. 1.25 hr

step-by-step explanation:

if you have a constant speed of 60 mph, then you have a ratio between 60 mi. to 1 hr. dividing both sides by 60 we get the ratio

1 mi. to

then mult. both sides by 75 we get the ratio

75 mi. to

simplifying we get

75 mi. to

or 1.25 hr.