Nine independent normal holding times have mean8.33 and standard deviation4.472. Sample mean M is normal. For the printed hypotheses H₀:M>6,Hₐ:M≤6,which expression gives the lower-tail/type-I probability at the stated population distribution?
The sample mean has standard error $4.472/\sqrt9=1.490667$. Standardizing threshold6 relative to mean8.33 gives $z=(6-8.33)/1.490667=-1.56306$,approximately−1.565 with source rounding. The lower-tail probability is therefore **A**. Strictly, hypotheses should refer to the population mean, not the random sample mean; this computes the stated lower-tail event under the given8.33 distribution.
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