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\begin{tabular}{|c|c|c|c|}$\newline$\hline Question $5$ , & ר & HW Score: $73.89 \%$, & \{్ర \\$\newline$\hline Part $3$ of $4$ & & (x) Points: $0$.$5$ of $1$ & Save \\$\newline$\hline$\newline$\end{tabular}$\newline$A simple random sample of size $n=14$ is obtained from a population with $\mu=69$ and $\sigma=16$.$\newline$(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of $\bar{x}$.$\newline$(b) Assuming the normal model can be used, determine $\mathrm{P}(\bar{x}<73.4)$.$\newline$(c) Assuming the normal model can be used, determine $P(\bar{x} \geq 70.7)$.$\newline$(a) What must be true regarding the distribution of the population?$\newline$A. Since the sample size is large enough, the population distribution doe need to be normal.$\newline$B. The sampling distribution must be assumed to be normal.$\newline$C. The population must be normally distributed.$\newline$D. The population must be normally distributed and the sample size must be large.$\newline$Assuming the normal model can be used, describe the sampling distribution $\bar{x}$. Choose the correct answer below.