Women’s heights are Normally distributed with a mean = 63.5 inches and a standard deviation = 2.5 inches. a) Using a relative frequency interpretation, interpret this probability by filling in the blanks: 45.15% of all _______ [units] have _____ [variable] between 63.0 and 64.0 inches. b) Without doing any computing, explain what happens to… …the distribution of the (sample) mean as the sample size increases. …the probability that the mean for the sampled women is between 63.0 and 64.0 as the sample size increases. c) suppose we know that in the population 15% of the women are overweight, what is the probability that in the sample of size 9, the proportion of women being overweight is bigger than 20% . Calculate the symmetrical interval that contains the sample proportion with 85% chance.
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!
Women’s heights are
- a) Using a relative frequency interpretation, interpret this
probability by filling in the blanks: 45.15% of all _______ [units] have _____ [variable] between 63.0 and 64.0 inches. - b) Without doing any computing, explain what happens to… …the distribution of the (sample) mean as the
sample size increases. …the probability that the mean for the sampled women is between 63.0 and 64.0 as the sample size increases. - c) suppose we know that in the population 15% of the women are overweight, what is the probability that in the sample of size 9, the proportion of women being overweight is bigger than 20% . Calculate the symmetrical interval that contains the sample proportion with 85% chance.
Step by step
Solved in 3 steps with 4 images
