The following histogram shows the relative frequencies of the heights, recorded to the nearest inch, of a population of women. The mean of the population is 64.97 inches, and the standard deviation is 2.66 inches. One woman from the population will be selected at random.

Question 3
(c) The histogram displays a discrete probability model for height. However, height is often considered a continuous variable that follows a normal model. Consider a normal model that uses the mean and standard deviation of the population of women as its parameters.

(i) Use the normal model and the relationship between area and relative frequency to find the probability that the randomly selected woman will have a height of at least 67 inches. Show your work.

(ii) Does your answer in part (c-i) match your answer in part (a) ? If not, give a reason for why the answers might be different.

Question 4
(d) Let the random variable H represent the height of a woman in the population. P(H<60) represents the probability of randomly selecting a woman with height less than 60 inches. Based on the information given, the probability can be found using either the discrete model or the normal model.

(i) Give an example of a probability of H that can be found using the discrete model but not the normal model. Explain why.

(ii) Give an example of a probability of H that can be found using the normal model but not the discrete model. Explain why.