Question

The number of vacation days taken by the employees of a company is normally distributed with a mean of 14 days and a standard deviation of 3 days. Is this a case of sample standard deviation or population standard deviation? What are some differences between sample standard deviation and population standard deviation?

For the next employee, what is the probability that the number of days of vacation taken is less than 10 days? What is the probability that the number of days of vacation taken is more than 21 days? Discuss the solutions and an explanation. Respond to your peers’ posts and offer your feedback on this topic.

Answer 1

Given that

Since sample size 'n' is unknown. You need not to worry whether its sample or population standard deviation. Consider the standard deviation given in the problem as population standard deviation or sample standard deviation. it's not going to affect the answer, Provided if n is unknown.

When to use sample or population standard deviation

The standard deviation is a measure of a score within a set of data. Usually, we are interested in knowing the population standard deviation because our population contains all the values we are interested in. Therefore we normally calculate the population standard deviation if you have the entire population or you have a sample of a larger population. Usually denoted by the letter ''.

You will calculate the sample standard deviation when a small proportion of the sample is drawn from the population. Usually denoted by the letter 's'.

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