A random sample of $n=64$ observations is drawn from a population with a mean equal to $17$ and a standard deviation equal to $16.$

a$.$ Find the probability that $\stackrel{}{x}$ is less than $13.$

b$.$ Find the probability that $\stackrel{}{x}$ is greater than $22.$

c$.$ Find the probability that $\stackrel{}{x}$ falls between $13$ and $19.$

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a$.$ The probability that $\stackrel{}{x}$ is less than $13$ is

$($Round to three decimal places as needed.$)$

b$.$ The probability that $\stackrel{}{x}$ is greater than $22$ is

$($Round to three decimal places as needed.$)$

c$.$ The probability that $\stackrel{}{x}$ falls between $13$ and $19$ is

$($Round to three decimal places as needed.$)$