Amachine is set to pump cleanser into a process at the rate of 8 gallons per minute. upon inspection, it is learned that the machine actually pumps cleanser at a rate described by the uniform distribution over the interval 7.5 to 10.5 gallons per minute. find the probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute.

The probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%

The Mean of the uniform distribution for an interval from a to b is given by the formula :

μ =

Here, the given interval is from 7.5 to 10.5 gallons per minute, that means a= 7.5 and b= 10.5

So, Mean(μ) =

Now, the standard deviation of the uniform distribution is given by the formula:

σ =

So, the standard deviation(σ) =

As we need to find the probability that between 8.0 gallons and 9.0 gallons are pumped, so now we will find z-score for both 8.0 and 9.0

The formula for z-score: z = (X - μ)/σ

So, z(X= 8.0) =

and z(X= 9.0) =

Now according to the z-score table, P(z=-1.1547) = 0.1251 and P(z=0) = 0.5

So, P(8.0 < x < 9.0)

= P(-1.1547 < z <0)

= 0.5 - 0.1251

= 0.3749

= 37.49%

Thus, the probability that between 8.0 gallons and 9.0 gallons are pumped during a randomly selected minute is 0.3749 or 37.49%

introduction, methodology, results, discussion

step-by-step explanation:

an observational study is one which consists of actual observation to record data and then analyse the data.

there are a number of factors that should be analyzed before starting an observational study.

the main four factors are:

i) introduction:   this should be analysed to check whether the purpose of the study is correctly established and the data recorded are appropriate for the study

methodology:   the method of collecting the data, such as whether randomly selected, and whether sample size matches with the population to be studied, whether questions asked are easy to answer by common men, etc.

results: then results such as summary of data with comments should be studied thoroughly

discussion:   the last is the discussion, this can be either by management people or persons who are all interested , etc.

its an acute right triangle

step-by-step explanation: