SOLUTION: The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary

Question 1162425: The Marine Corps is ordering hats for all the new recruits for the entire next year. Since they do not know the exact hat sizes they will use statistics to calculate the necessary numbers.
This is the data from a sample of the previous recruits:
7.2, 6.8, 6, 6.9, 7.8, 6.2, 6.4, 7.2, 7.4, 6.8, 6.7, 6, 6.4, 7, 7, 7.6, 7.6, 6, 6.8, 6.4
a. Display the data in a line plot and stem-and-leaf plot. (These plots don’t need to be pretty; just make sure I can make sense of your plots.) Describe what the plots tell you about the data.
b. Find the mean, median, mode, and range.
c. Is it appropriate to use a normal distribution to model this data?
d. Suppose that the Marine Corps does know that the heights of new recruits are approximately normally distributed with a mean of 70.5 inches and a standard deviation of 1.5 inches. Use the mean and standard deviation to fit the new recruit heights to a normal distribution and estimate the following percentages.
d1. What percent of new recruits would be taller than 72 inches?
d2. What percent of new recruits would be shorter than 67.5 inches?
d3. What percent of new recruits would be between 69 and 72 inches?
d4. Between what two heights would capture 95% of new recruits??
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
6/0xxx
6/2x
6/4xxx
6/6
6/7x
6/8xxx
6/9x
7/0xx
7/2xx
7/4x
7/6xx
7/8x
Rotate the data 90 degrees. It doesn't appear normal. It has does have modes at 6.0, 6.4, and 6.8, and it is a little bit uniform.
mean is 6.81
median is half way between the 10th and 11th of ordered values. Both of them are 6.8, so that is the median.
range is 1.8 (7.8-6.0)
z=(x-mean)/sd
so the first is (72-70.5)/1.5 and want z>1 which is 0.1587 probability
shorter than 67.5 inches is z<-2 or 0.0228 probability
between 69 and 72 inches is -1 95% are between +/-2 sds or +/-3 inches or (67.5, 73.5 inches)
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