Suppose a student carrying a flu virus returns to an isolated college campus of 6000 students. Determine a differential equation
1 answer:
Answer:
Step-by-step explanation:
Total Number of Students =6000
Number of students who have contracted the flu =x(t)
Number of students who have not contracted the flu =6000- x(t)
Now, the rate at which the disease spreads is proportional to the number of interactions between students with the flu and students who have not yet contracted it.
Initially, the campus is uninfected, therefore: x(0)=0
Therefore, a differential equation governing the number of students x(t) who have contracted the flu is:
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Complete Question
Problem 7.43
A chemical plant superintendent orders a process readjustment (namely shutdown and setting change) whenever the pH of the final product falls below 6.92 or above 7.08. The sample pH is normally distributed with unknown mu and standard deviation 0.08. Determine the probability:
(a)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is operating as intended and = 7.0 probability
(b)
of readjusting (that is, the probability that the measurement is not in the acceptable region) when the process is slightly off target, namely the mean pH is = 7.02
Answer:
a
The value is
b
The value is
Step-by-step explanation:
From the question we are told that
The mean is
The standard deviation is
Considering question a
Generally the probability of readjusting when the process is operating as intended and mu 7.0 is mathematically represented as
=>
Generally
So
=>
=>
From the z table the probability of (Z < -1.25) and (Z > 1 ) is
and
So
=>
=>
Considering question b
Generally the probability of readjusting when the process is operating as intended and mu 7.02 is mathematically represented as
=>
Generally
So
=>
=>
From the z table the probability of (Z < -1.5) and (Z > 0.75 ) is
and
So
=>
=>