A sample of size $42$ will be drawn from a population with mean $52$ and standard deviation $11.$ Use the TI Inspire calculator.

$($a$)$ Is it appropriate to use the normal distribution to find probabilities for $\stackrel{}{x}?$

$($b$)$ Find the probability that $\stackrel{}{x}$ will be between $53$ and $54.$ Round the answer to at least four decimal places.

$($c$)$ Find the ${46}^{th}$ percentile of $\stackrel{}{x}.$ Round the answer to at least two decimal places.

It is appropriate to use the normal distribution to find probabilities for $\stackrel{}{x}.$

The probability that $\stackrel{}{x}$ will be between $53$ and $54$ is The ${46}^{th}$ percentile of $\stackrel{}{x}$ is

It is not appropriate to use the normal distribution to find probabilities for $\stackrel{}{x}.$

Please solve with TI Inspire steps