What is the circumference of the semicircle in this figure? Express your answer in feet.
1 answer:
You might be interested in
Answer:
a)
b)
And using a calculator, excel ir the normal standard table we have that:
c) Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let X the random variable that represent the female pulse rates of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
And the best way to solve this problem is using the normal standard distribution and the z score given by:
If we apply this formula to our probability we got this:
Part b
The central limit theorem states that "if we have a population with mean μ and standard deviation σ and take sufficiently large random samples from the population with replacement, then the distribution of the sample means will be approximately normally distributed. This will hold true regardless of whether the source population is normal or skewed, provided the sample size is sufficiently large".
From the central limit theorem we know that the distribution for the sample mean is given by:
The new z score is given by:
And using a calculator, excel ir the normal standard table we have that:
Part c
c. Why can the normal distribution be used in part (b), even though the sample size does not exceed 30?
Since the original population has a normal distribution, the distribution of sample means is a normal distribution for any sample size.