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Sagot :
Given data
*The given mean is
[tex]\mu=18.6[/tex]*The given standard deviation is
[tex]\sigma=5.9[/tex]The value of the z score is calculated as
[tex]z=\frac{x-\mu}{\sigma}[/tex]Substitute the values in the above expression as
[tex]\begin{gathered} z=\frac{21-18.6}{5.9} \\ =0.41 \end{gathered}[/tex]The probability that the mean score of an SRS of 40 students chosen from all those taking the test is 21 or higher is given as
[tex]\begin{gathered} P(Z\ge21)=P(X\ge0.41) \\ =1-P(X<0.41) \end{gathered}[/tex]The corresponding probability is evaluated by the table.
Substitute the values in the above expression as
[tex]\begin{gathered} P(Z\ge21)=1-0.6591 \\ =0.34 \end{gathered}[/tex]
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