SOLUTION: . The Marine Corp 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 necessar

Question 1083615: . The Marine Corp 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, assume the numbers are normally distributed.
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 Corp 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!
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This is a stem and leaf plot.
mean is 138.2/20=6.91
median of 20 is half way between 10th and 11th or an ordered plot. The 10th and the 11th are both 6.8, so that is the median.
6.4 and 6.8 are modes, but they are so minimal I would say there isn't a clear mode.
The range is 1.8, the largest-the smallest
This is not a normal distribution.
z=(x-mean) sd
a.(72-70.5)/1.5=1 so z>1 is the probability or 0.1587.
b.shorter than 67.5 inches is (67.5-70.5)/1.5 or z < = -2, and probability is 0.0228.
c.Between 69 and 72 inches is +/- 1 sd or 0.6826.
95% is 1.96 sd s on either side or +/- 1.96*1.5=+/- 2.94 interval on either side of 70.5
(67.56, 73.44)units in inches

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