Question

Laboratory data show that the time required to complete two chemical reactions in a production process varies. the first reaction has a mean time of 40 minutes and a standard deviation of 2 minutes; the second has a mean time of 25 minutes and a standard deviation of 1 minute. the two reactions are run in sequence during production. there is a period of 5 minutes between the two reactions as the product of the first reaction is pumped into the vessel where the second reaction will take place.
a. what is the mean time required for the entire process?
b. what is the standard deviation of the combined process?

Answer 1

For the answer to the question above,
For a) Mean time required for the entire process = (40+25) = 65 minutes
b) Variance time required for the entire process = (2^2+1^2) = 5 minutes
Standard deviation time required for the entire process = sqrt(5) = 2.236 minute.
I hope my answer helped you

Answer 2

Answer: a) Mean = 70;  b) Standard Deviation = 2.236

Step-by-step explanation: Mean is the average value of a data set, while standard deviation is how spread out the numbers are from the mean.

a) The first reaction has a meantime of 40 minutes, while the second reaction's mean is 25 minutes. There is a 5 minutes period between reactions.

So, the mean for both reactions is:

μ = 40 + 25 + 5

μ = 70

The mean time is 70 minutes.

b) The standard deviation is a square root of a sum of square numbers. Each reaction has their own already found standard deviation, so:

SD = $\sqrt{2^{2} + 1^{2} }$

SD = $\sqrt{5}$

SD = 2.236

The standard deviation is 2.236.