What is the common difference d of the sequence?
2 answers:
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Answer:
The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.
Step-by-step explanation:
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.
For the population, we have that:
Mean = 15
Standard deviaiton = 12
Sample of 30
By the Central Limit Theorem
Mean 15
Standard deviation
Approximately normal
The sampling distribution of the sample mean of size 30 will be approximately normal with mean 15 and standard deviation 2.19.
a.
In order to find the common ratio, we just need to divide a term by the term that comes before it.
So using the terms 20 and -5, we have:
b.
The recursive rule can be found with the formula:
Where an is the nth term and q is the ratio. So we have:
c.
The explicit rule can be written as:
Where an is the nth term, a1 is the first term and q is the ratio. So: