Answer:
The mean until the supplement is published is 140 months, while the standard deviation is of 11.8 months.
Step-by-step explanation:
The Poisson distribution is used to solve this question, as we have only the mean. In this distribution, the standard deviation is the square root of the mean.
In this question, we have that:
Species are discovered at a rate of once every 7 months.
A supplement to a guide is planned to be published after 20 new species have been discovered.
a) What are the expected value and standard deviation of the number of months (treated as a continuous measure of time) until the supplement is published?
Mean is: 7*20 = 140 months.
Standard deviation is = 11.8 months.
The mean until the supplement is published is 140 months, while the standard deviation is of 11.8 months.
Answer:
a) p-hat (sampling distribution of sample proportions)
b) Symmetric
c) σ=0.058
d) Standard error
e) If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).
Step-by-step explanation:
a) This distribution is called the <em>sampling distribution of sample proportions</em> <em>(p-hat)</em>.
b) The shape of this distribution is expected to somewhat normal, symmetrical and centered around 16%.
This happens because the expected sample proportion is 0.16. Some samples will have a proportion over 0.16 and others below, but the most of them will be around the population mean. In other words, the sample proportions is a non-biased estimator of the population proportion.
c) The variability of this distribution, represented by the standard error, is:
d) The formal name is Standard error.
e) If we divided the variability of the distribution with sample size n=90 to the variability of the distribution with sample size n=40, we have:
If we increase the sample size from 40 to 90 students, the standard error becomes two thirds of the previous standard error (se=0.667).