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Sagot :
Solution:
Given:
[tex]\begin{gathered} \mu=70 \\ \sigma=8 \\ n=16 \\ x=77 \end{gathered}[/tex]Using the Z-score formula;
[tex]Z=\frac{x-\mu}{\frac{\sigma}{\sqrt{n}}}[/tex]Substituting the values to get the Z-score,
[tex]\begin{gathered} Z=\frac{77-70}{\frac{8}{\sqrt{16}}} \\ Z=\frac{7}{\frac{8}{4}} \\ Z=\frac{7}{2} \\ Z=3.5 \end{gathered}[/tex]The probability that the mean of the test scores is less than 77 is gotten from Z-score tables.
From the Z-score table,
[tex]P(xTherefore, the probability that the mean of the test scores is less than 77 is approximately 0.9998
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