According to the WHO MONICA Project the mean blood pressure for people in China is 128 mmHg with a standard deviation of 23 mmHg (Kuulasmaa, Hense & Tolonen, 1998). Blood pressure is normally distributed. Suppose a sample of size 15 is taken. State the shape of the distribution of the sample mean. Suppose a sample of size 15 is taken. State the mean of the sample mean. Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
According to the WHO MONICA Project the
- Suppose a
sample of size 15 is taken. State the shape of the distribution of the sample mean. - Suppose a sample of size 15 is taken. State the mean of the sample mean.
- Suppose a sample of size 15 is taken. State the standard deviation of the sample mean.
Introduction:
The sampling distribution of the sample mean, X̄, based on a sample of size n, taken from a population with expectation μ and standard deviation σ, has expectation μX̄ = μ and standard deviation σX̄ = σ/√n.
If the sample size is large (n ≥ 30), or the population distribution is normal, then by the central limit theorem, the sampling distribution of the sample mean is normal, with parameters μX̄ and σX̄.
Trending now
This is a popular solution!
Step by step
Solved in 2 steps
