Welcome to Bytelearn!

Let’s check out your problem:

A simple random sample of size $n$ is drawn from a population that is normally distributed. The sample mean, $\bar{x}$, is found to be $17$.$6$ , and the sample standard deviation, $s$, is found to be $5$.$7$ .$\newline$(a) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, $n$, is $39$ .$\newline$(b) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, $n$, is $67$ .$\newline$How does increasing the sample size affect the margin of error, $E$ ?$\newline$(c) Construct a $\bar{x}$$0$ confidence interval about $\mu$ if the sample size, $n$, is $39$ . How does increasing the level of confidence affect the size of the margin of error, $E$ ?$\newline$(d) If the sample size is $18$ , what conditions must be satisfied to compute the confidence interval?$\newline$(a) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, $n$, is $39$ .$\newline$Lower bound: $16$.$06$ ; Upper bound: $19$.$14$$\newline$(Round to two decimal places as needed.)$\newline$(b) Construct a $90 \%$ confidence interval about $\mu$ if the sample size, $n$, is $67$ .$\newline$Lower bound: $s$$0$ ; Upper bound: $s$$0$$\newline$(Round to two decimal places as needed.)