# Computing Probability Under Normal Distribution and Conducting

Please look at the 3 attached files for the computing probability problems.

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#### Solution Preview

Problem 1

(a) We need to calculate the mean and standard deviation of the 15 data.

Mean=(11+3+...-5+2)/18=1.89

Variance=[(11-1.89)2+(3-1.89)2+...+(-5-1.89)2+(2-1.89)2]/(18-1)=16.46

Standard deviation=sqrt(16.46)=4.06.

Hence, if a number is usual, it must be within 2 standard deviations about mean.

It is within the interval (1.89-2*4.06, 1.89+2*4.06)=(-6.23, 10.01).

Since 15 is not ...

#### Solution Summary

The solution gives detailed steps on 3 questions focused on computing probability under normal distribution and conducting hypothesis testing under t distribution.

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