Which algebraic expression is equivalent to the expression below?
2 answers:
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Answer:
The number of bacteria after
days is given by
where is the initial number of bacteria.
Step-by-step explanation:
The number of bacteria in the sample triples every 10 days, this means after the first 10th day, the number of bacteria is
where is the initial number of bacteria in the sample.
After the 2nd 10th days, the number of bacteria is
after the 3rd day,
and so on.
Thus, the formula we get for the number of bacteria after the <em>n</em>th 10-days is
where is is the <em>n</em>th 10-days.
Since, is 10 days, we have
or
Substituting that into , we get:
Answer:
The mean is 95 and the standard deviation is 2
Step-by-step explanation:
Central Limit Theorem
The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean and standard deviation
, the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean
and standard deviation
.
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
In this question:
Population:
Mean 95, Standard deviation 12
Samples of size 36:
By the Central Limit Theorem,
Mean 95
Standard deviation