Problem #$3$

You must use the empirical rule to answer the problems in this question. In other words, I do not want you to use R$\text{'}$s pnorm$()$ function to answer any of these questions. The only exception is if a specific problem asks you to use $R.$

Another set of latency tests yielded an approximately normally distributed set of observations: $N(10\mathrm{.}2,2\mathrm{.}4)$

One ping was $7\mathrm{.}8$ nanoseconds. What percentage of pings are shorter than this time?

One ping was $17\mathrm{.}4$ nanoseconds. What percentage of pings are higher $($longer$)?$

What percentage of pings are between $7\mathrm{.}8$ and $15$ nanoseconds?

What percentage of pings would be shorter than $5\mathrm{.}4$ nanoseconds?

One ping had a time corresponding to a $z-$score of $+3.$ What was this time?

Do not use the empirical rule for this problem. Instead, use R for a precise calculation. One result was in the $90$ th percentile. What time does this correspond to$?$ Hint: There is an $R$ function that will give you this exact piece of information. That is$,$ it converts the area under the normal density curve back into a z$-$score.