Use normal sampling distributions and standard errors
Use exact values except for an explicitly requested four-decimal probability. X̄ denotes the random sample mean; x̄ is one realised value
X₁,...,Xₙ are independent observations from the same normal population. The second normal parameter below is the variance
\[X_i\sim N(5,9),\qquad n=49,\qquad\overline X=\frac1n\sum_{i=1}^nX_i\]
\[b=\frac{38}{7}\]
Compare the same raw boundary b for one individual observation and for the sample mean. Use the appropriate standard deviation in each standard score