Question: Tall girls According to the National Center for Health Statistics, the distribution of heights for 16-year-old females is modeled well by a Normal density curve with mean μ = 64 inches and standard deviation σ = 2.5 inches. To see if this distribution applies at their high school, an AP® Statistics class takes an SRS of 20 of the 300 16-year-old females at the school and measures their heights. What values of the sample mean x - would be consistent with the population distribution being N(64, 2.5)? To find out, we used Fathom software to simulate choosing 250 SRSs of size n = 20 students from a population that is N(64, 2.5). The figure below is a dotplot of the sample mean height x - of the students in each sample.
![2346_xbar.png](https://secure.tutorsglobe.com/CMSImages/2346_xbar.png)
(a) There is one dot on the graph at 62.4. Explain what this value represents.
(b) Describe the distribution. Are there any obvious outliers?
(c) Would it be surprising to get a sample mean of 64.7 or more in an SRS of size 20 when m = 64? Justify your answer.
(d) Suppose that the average height of the 20 girls in the class's actual sample is x - = 64.7. What would you conclude about the population mean height m for the 16-year-old females at the school? Explain.