1. The USGA announced that they are going to be very "tough" in enforcing the rule that the maximum coefficient of restitution (COR) for golf club drivers be 0.83.(some drivers were measured by them as 0.85, this COR gives a drive 5 yards or so advantage over one that is "in spec."Assume that the lower spec limit is 0.70)

2. The USGA will allow the upper spec limit on any manufacturer's driver to be 0.83 as long as the Cpk is at least 2.0.Ping has developed a very repeatable process for making the driver heads that they believe can achieve a Cpk of 2 with the average COR being 0.828.

a)If this is true what must s be?

b)Ping is encouraged as they believe their competitors s is at least 0.004.If this is true, what COR average must the competitor aim for to have a Cpk = 2.

c)every 0.01 loss in COR the driver loses 2.5 yards.How much less yardage will the competitions driver hit a ball on average as compared to Pings?

d)Ping manufactures 10,000 drivers.The data are in the spreadsheet in tab "Golf Club COR" .Analyze the data.Assume with subgroup size = 1.Did they achieve their goal?Comment on the data Re: normality, etc.Are there Shewhart violations?If so discuss them.State any assumptions.the appropriate data and/or graphs are below. Use an upper spec of 0.83 and a lower spec of 0.82.

Golf Club COR 0.82709 0.82805 0.82774 0.82826 0.82806 0.82798 0.82788 0.82838 0.82828 0.82820 0.82772 0.82832 0.82817 0.82801 0.82785 0.82735 0.82760 0.82790 0.82769 0.82771 0.82868 0.82796 0.82765 0.82722 0.82729 0.82791 0.82802 0.82805 0.82808 0.82808 0.82771 0.82813 0.82796 0.82789 0.82753 0.82808 0.82824 0.82826 0.82801 0.82784 0.82835 0.82818 0.82851 0.82843 0.82803 0.82768 0.82797 0.82778 0.82833 0.82776 0.82823 0.82830 0.82882 0.82903 0.82808 0.82792 0.82781 0.82784 0.82830 0.82741 0.82791 0.82760 0.82814 0.82752 0.82729 0.82842 0.82782 0.82782 0.82807 0.82815 0.82830 0.82818 0.82799 0.82775 0.82820 0.82798 0.82797 0.82849 0.82820 0.82763 0.82808 0.82791 0.82819 0.82808 0.82805 0.82789 0.82769 0.82777 0.82794 0.82826 0.82801 0.82870 0.82820 0.82788 0.82771 0.82812 0.82799 0.82754 0.82816 0.82800 0.82769 0.82849 0.82768 0.82839 0.82815 0.82785 0.82794 0.82756 0.82855 0.82814 0.82769 0.82835 0.82828 0.82806 0.82774 0.82772 0.82827 0.82798 0.82770 0.82800 0.82819 0.82793 0.82782 0.82805 0.82814 0.82821 0.82818 0.82798 0.82765 0.82790 0.82829 0.82746 0.82801 0.82813 0.82794 0.82762 0.82849 0.82842 0.82804 0.82788 0.82798 0.82790 0.82831 0.82786 0.82797 0.82782 0.82864 0.82784 0.82819 0.82805 0.82774 0.82821 0.82830 0.82792 0.82800 0.82837 0.82742 0.82877 0.82805 0.82751 0.82802 0.82774 0.82830 0.82810 0.82812 0.82775 0.82830 0.82765 0.82763 0.82820 0.82785 0.82847 0.82783 0.82787 0.82768 0.82819 0.82829 0.82816 0.82808 0.82820 0.82780 0.82768 0.82712 0.82754 0.82826 0.82831 0.82776 0.82764 0.82804 0.82734 0.82764 0.82797 0.82820 0.82815 0.82803 0.82757 0.82795 0.82775 0.82815 0.82783 0.82795 0.82778 0.82806 0.82802 0.82810 0.82770 0.82800 0.82854 0.82815 0.82843 0.82774 0.82787 0.82772 0.82878 0.82797 0.82886 0.82761 0.82810 0.82761 0.82795 0.82845 0.82750 0.82838 0.82783 0.82778 0.82822 0.82793 0.82775 0.82810 0.82808 0.82796 0.82797 0.82807 0.82810 0.82832 0.82828 0.82810 0.82818 0.82805 0.82790 0.82773 0.82819 0.82804 0.82839 0.82779 0.82774 0.82808 0.82816 0.82806 0.82789 0.82800 0.82758 0.82819 0.82809 0.82809 0.82815 0.82826 0.82769 0.82806 0.82833 0.82841 0.82809 0.82818 0.82749 0.82813 0.82860 0.82786 0.82805 0.82785 0.82772 0.82763 0.82834 0.82831 0.82820 0.82770 0.82787 0.82758 0.82757 0.82811 0.82827 0.82803 0.82796 0.82793 0.82784 0.82797 0.82800 0.82769 0.82786 0.82819 0.82785 0.82828 0.82852 0.82834 0.82818 0.82784 0.82848 0.82766 0.82755 0.82824 0.82802 0.82808 0.82851 0.82756 0.82835 0.82812 0.82786 0.82762 0.82800 0.82778 0.82783 0.82842 0.82804 0.82813 0.82764 0.82799 0.82791 0.82800 0.82825 0.82801 0.82791 0.82815 0.82802 0.82808 0.82792 0.82724 0.82816 0.82762 0.82809 0.82833 0.82799 0.82820 0.82800 0.82791 0.82824 0.82804 0.82789 0.82851 0.82810 0.82772 0.82790 0.82766 0.82820 0.82850 0.82809 0.82743 0.82787 0.82752 0.82811 0.82766 0.82831 0.82833 0.82807 0.82818 0.82832 0.82735 0.82766 0.82816 0.82809 0.82777 0.82755 0.82771 0.82809 0.82788 0.82786 0.82790 0.82812 0.82826 0.82826 0.82802 0.82808 0.82825 0.82839 0.82768 0.82810 0.82793 0.82780 0.82767 0.82832 0.82755 0.82795 0.82806 0.82784 0.82804 0.82777 0.82785 0.82763 0.82826 0.82767 0.82783 0.82824 0.82838 0.82824 0.82820 0.82809 0.82789 0.82832 0.82778 0.82833 0.82778 0.82780 0.82803 0.82865 0.82752 0.82758 0.82802 0.82794 0.82761 0.82781 0.82837 0.82778 0.82768 0.82766 0.82845 0.82758 0.82750 0.82753 0.82787 0.82841 0.82792 0.82795 0.82848 0.82829 0.82803 0.82830 0.82815 0.82792 0.82781 0.82721 0.82802 0.82851 0.82792 0.82779 0.82806 0.82780 0.82814 0.82848 0.82795 0.82837 0.82727 0.82847 0.82808 0.82824 0.82806 0.82768 0.82777 0.82791 0.82721 0.82794 0.82758 0.82812 0.82832 0.82755 0.82826 0.82813 0.82815 0.82826 0.82802 0.82815 0.82768 0.82815 0.82818 0.82823 0.82744 0.82834 0.82811 0.82816 0.82759 0.82804 0.82849 0.82753 0.82782 0.82768 0.82863 0.82809 0.82784 0.82843 0.82790 0.82815 0.82777 0.82770 0.82779 0.82802 0.82839 0.82763 0.82839 0.82796 0.82758 0.82823 0.82772 0.82858 0.82823 0.82834 0.82776 0.82797 0.82720 0.82820 0.82764 0.82793 0.82785 0.82873 0.82747 0.82780 0.82774 0.82780 0.82769 0.82809 0.82836 0.82846 0.82774 0.82823 0.82811 0.82812 0.82840 0.82797 0.82842 0.82813 0.82769 0.82810 0.82805 0.82794 0.82847 0.82803 0.82806 0.82803 0.82780 0.82792 0.82788 0.82746 0.82825 0.82774 0.82756 0.82792 0.82807 0.82756 0.82775 0.82770 0.82811 0.82797 0.82808 0.82816 0.82796 0.82814 0.82792 0.82829 0.82807 0.82775 0.82849 0.82835 0.82792 0.82867 0.82773 0.82838 0.82806 0.82796 0.82810 0.82816 0.82751 0.82783 0.82781 0.82793 0.82838 0.82817 0.82818 0.82838 0.82792 0.82792 0.82839 0.82785 0.82791 0.82805 0.82789 0.82819 0.82820 0.82819 0.82819 0.82767 0.82775 0.82782 0.82814 0.82840 0.82790 0.82801 0.82763 0.82840 0.82775 0.82801 0.82812 0.82795 0.82815 0.82760 0.82758 0.82757 0.82743 0.82789 0.82785 0.82815 0.82768 0.82792 0.82755 0.82814 0.82818 0.82775 0.82815 0.82809 0.82812 0.82803 0.82761 0.82803 0.82751 0.82859 0.82797 0.82856 0.82818 0.82802 0.82814 0.82815 0.82790 0.82792 0.82751 0.82826 0.82771 0.82754 0.82785 0.82824 0.82776 0.82786 0.82799 0.82729 0.82795 0.82801 0.82808 0.82821 0.82792 0.82788 0.82830 0.82847 0.82809 0.82883 0.82752 0.82805 0.82833 0.82791 0.82785 0.82783 0.82742 0.82809 0.82792 0.82738 0.82744 0.82797 0.82832 0.82846 0.82793 0.82818 0.82809 0.82826 0.82835 0.82806 0.82807 0.82758 0.82825 0.82797 0.82807 0.82807 0.82805 0.82827 0.82813 0.82788 0.82730 0.82781 0.82788 0.82778 0.82822 0.82790 0.82834 0.82764 0.82818 0.82810 0.82837 0.82773 0.82803 0.82839 0.82823 0.82854 0.82774 0.82839 0.82825 0.82850 0.82831 0.82837 0.82810 0.82773 0.82809 0.82781 0.82780 0.82819 0.82824 0.82771 0.82817 0.82799 0.82758 0.82826 0.82832 0.82765 0.82785 0.82806 0.82798 0.82821 0.82774 0.82818 0.82877 0.82735 0.82811 0.82815 0.82772 0.82756 0.82782 0.82814 0.82830 0.82804 0.82790 0.82823 0.82778 0.82811 0.82778 0.82775 0.82857 0.82783 0.82740 0.82822 0.82769 0.82750 0.82729 0.82788 0.82811 0.82788 0.82794 0.82794 0.82760 0.82803 0.82816 0.82787 0.82812 0.82835 0.82803 0.82805 0.82752 0.82797 0.82781 0.82794 0.82833 0.82799 0.82759 0.82805 0.82817 0.82823 0.82833 0.82831 0.82784 0.82833 0.82811 0.82820 0.82828 0.82822 0.82834 0.82840 0.82841 0.82802 0.82795 0.82763 0.82789 0.82828 0.82795 0.82771 0.82706 0.82812 0.82823 0.82754 0.82760 0.82791 0.82814 0.82826 0.82769 0.82768 0.82750 0.82788 0.82737 0.82861 0.82811 0.82752 0.82841 0.82811 0.82795 0.82739 0.82779 0.82792 0.82812 0.82823 0.82740 0.82828 0.82767 0.82810 0.82804 0.82864 0.82797 0.82776 0.82784 0.82823 0.82788 0.82799 0.82808 0.82762 0.82865 0.82821 0.82769 0.82797 0.82817 0.82891 0.82823 0.82811 0.82809 0.82848 0.82815 0.82783 0.82805 0.82783 0.82804 0.82817 0.82779 0.82804 0.82799 0.82850 0.82813 0.82822 0.82809 0.82796 0.82825 0.82820 0.82869 0.82775 0.82810 0.82840 0.82807 0.82842 0.82800 0.82799 0.82796 0.82837 0.82847 0.82773 0.82780 0.82775 0.82818 0.82847 0.82810 0.82748 0.82811 0.82745 0.82804 0.82803 0.82796 0.82754 0.82880 0.82766 0.82808 0.82751 0.82772 0.82812 0.82787 0.82786 0.82812 0.82793 0.82795 0.82777 0.82814 0.82771 0.82800 0.82801 0.82826 0.82795 0.82722 0.82788 0.82791 0.82766 0.82828 0.82819 0.82837 0.82811 0.82812 0.82801 0.82819 0.82819 0.82852 0.82797 0.82790 0.82764 0.82839 0.82828 0.82797 0.82763 0.82834 0.82821 0.82747 0.82794 0.82846 0.82755 0.82771 0.82776 0.82764 0.82807 0.82765 0.82809 0.82806 0.82815 0.82819 0.82841 0.82813 0.82784 0.82826 0.82791 0.82884 0.82822 0.82775 0.82771 0.82791 0.82773 0.82806 0.82774 0.82853 0.82774 0.82791 0.82785 0.82765 0.82775 0.82750 0.82822 0.82821 0.82835 0.82713 0.82796 0.82794 0.82825 0.82797 0.82800 0.82820 0.82779 0.82804 0.82760 0.82843 0.82837 0.82832 0.82753 0.82799 0.82810 0.82820 0.82821 0.82780 0.82840 0.82824 0.82775 0.82804 0.82751 0.82802 0.82824 0.82816 0.82741 0.82819 0.82804 0.82841 0.82835 0.82825 0.82785 0.82792 0.82799 0.82751 0.82812 0.82706 0.82822 0.82821 0.82777 0.82770 0.82753 0.82813 0.82745 0.82788 0.82816 0.82825 0.82795 0.82863 0.82810 0.82784 0.82798 0.82834 0.82758 0.82762 0.82768 0.82768 0.82842 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