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
\[X_i\sim N(5,4),\qquad n=25,\qquad\overline X=\frac1n\sum_{i=1}^nX_i\]
\[\text{Find }\Pr(\overline X<\frac{27}{5})\]
Give the probability to four decimal places, rounding only after forming the complete tail or interval