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A study of college football games shows that the number of holding penalties assessed has a mean of 2.3 penalties per game and a standard deviation of 1.1 penalties per game.What is the probability that, for a sample of 40 college games to be played next week, the mean number of holding penalties will be 2.35 penalties per game or more?Carry your intermediate computations to at least four decimal places. Round your answer to at least three decimal places.



Answer :

We know:

[tex]\begin{gathered} \bar{x}=2.35 \\ S=1.1 \\ n=40 \\ \mu=2.3 \end{gathered}[/tex]

The probability is:

[tex]t=\frac{\bar{x}-\mu}{\frac{s}{\sqrt{n}}}=\frac{2.3-2.35}{\frac{1.1}{\sqrt{40}}}=0.2875[/tex]

Then, from the normal distribution table:

[tex]\begin{gathered} 0.28\rightarrow0.6103 \\ 0.29\rightarrow0.6141 \end{gathered}[/tex]

Now we compute the values in the calculator for the obtained value:

[tex]0.2875\rightarrow0.613[/tex]

The probability is 0.613.

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