The probability of mean weight [tex]642[/tex] gram is [tex]p=0.0990[/tex]
The probability of mean weight [tex]657[/tex] gram is [tex]p=0.9946[/tex]
Given Equation:
Mean [tex]=651[/tex]
Standard deviation [tex]=27[/tex]
n[tex]=49[/tex]
The general form of,
[tex]z=\frac{x -\mu}{\sigma\ /\sqrt{n} }[/tex]
Probability of [tex]657[/tex]:
By given,
[tex]x=642\\\sigma=27\\n=49\\\mu = 651\\[/tex]
Substitute the values in the general form,
[tex]z=\frac{642-651}{27/\sqrt{49} } \\\\z=\frac{-9}{27/7} } \\\\z=\frac{-9}{3.86} \\\\z=-2.331[/tex]
[tex]p=0.0990[/tex]
Probability of [tex]657[/tex]:
By given,
[tex]x=657\\\sigma=27\\n=49\\\mu = 651\\[/tex]
Substitute the values in the general form,
[tex]z=\frac{657-651}{27/\sqrt{49} } \\\\z=\frac{6}{27/7} } \\\\z=\frac{6}{3.86} \\\\z=1.55[/tex]
[tex]p=0.9946[/tex]
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