Suppose that I have the ability to take a random sample of $100$ SMSU students and force them to take a statistics test. Further suppose that I actually go through with such a plan and score all $100$ tests. If I were to test all students and score their tests, I would find a mean of $65$ and a standard deviation of $5.$

a$.$ Show calculations for the mean and standard deviation of the sampling distribution for x$-$bar for the sample of $100$ students.

b$.$ Calculate the probability that when I take the random sample of $100$ students I find an x$-$bar greater than $70.$ That is calculate P$($x$-$bar $>70).$

c$.$ Calculate P$($x$-$bar $<mtext\; id="EditorElement\_268754"></mtext><mn\; id="EditorElement\_268755">5</mn><mn\; id="EditorElement\_268756">5</mn><mi\; id="EditorElement\_268757">)</mi>$ for this sample of $100$ students.

d$.$ If SMSU$$s continued funding from the state government depended on finding that more than $50\%$ of students could pass a statistics test with a score of $60$ or more, wo

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