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Start Spring $2024$$\newline$Question $5$,$\newline$HW Score: $73.89 \%$,$\newline$$8$.$1$.$17$-T$\newline$$4$.$43$ of $6$ points$\newline$Part $4$ of $4$$\newline$Points: $0$.$5$ of $1$$\newline$Save$\newline$A simple random sample of size $n=10$ is obtained from a population with $\mu=63$ and $\sigma=15$.$\newline$(a) What must be true regarding the distribution of the population in order to use the normal model to compute probabilities involving the sample mean? Assuming that this condition is true, describe the sampling distribution of $\bar{x}$.$\newline$(b) Assuming the normal model can be used, determine $\mathrm{P}(\bar{x}<66.4)$.$\newline$(c) Assuming the normal model can be used, determine $P(x \geq 64.2)$.$\newline$(a) What must be true regarding the distribution of the population?$\newline$A. The sampling distribution must be assumed to be normal.$\newline$B. Since the sample size is large enough, the population distribution doe need to be normal.$\newline$C. The population must be normally distributed and the sample size must be large.$\newline$D. The population must be normally distributed.$\newline$Assuming the normal model can be used, describe the sampling distribution $\bar{x}$. Choose the correct answer below.$\newline$A. Normal, with $\mu_{\bar{x}}=63$ and $\sigma_{\bar{x}}=15$$\newline$B. Normal, with $\mu_{\bar{x}}=63$ and $n=10$$1$$\newline$C. Normal, with $\mu_{\bar{x}}=63$ and $n=10$$3$$\newline$(b) $n=10$$4$ (Round to four decimal places as needed.)$\newline$(c) $n=10$$5$ (Round to four decimal places as needed.)