In: Statistics and Probability
Blood pressure readings are normally distributed with a mean of 120 and a standard deviation of 8.
a. If one person is randomly selected, find the probability that their blood pressure will be greater than 125.
b. If 16 people are randomly selected, find the probability that their mean blood pressure will be greater than 125. 5
c. Why can the central limit theorem be used in part (b.), even that the sample size does not exceed 30?
a.
b.
c.
The central limit theorem states that if you 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 (usually n > 30). If the population is normal, then the theorem holds true even for samples smaller than 30. In fact, this also holds true even if the population is binomial, provided that min(np, n(1-p))> 5, where n is the sample size and p is the probability of success in the population.
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