The proportion of left-handed people in the general population is about 0.1. Suppose a random sample of 225 people is observed.
1. What is the sampling distribution of the sample proportion (p-hat)? In other words, what can we say about the behavior of the different possible values of the sample proportion that we can get when we take such a sample?
(Note: normal approximation is valid because .1(225) = 22.5 and .9(225) = 202.5 are both more than 10.)
2. Since the sample proportion has a normal distribution, its values follow the Standard Deviation Rule. What interval is almost certain (probability .997) to contain the sample proportion of left-handed people?
3. In a sample of 225 people, would it be unusual to find that 40 people in the sample are left-handed?
4. Find the approximate probability of at least 27 in 225 (proportion .12) being left-handed. In other words, what is P(p-hat ? 0.12)?
Guidance: Note that 0.12 is exactly 1 standard deviation (0.02) above the mean (0.1). Now use the Standard Deviation Rule.
