Rounding instructions:

Use your graphing calculator. If you get a decimal answer, round to four decimal places. If you get an answer in scientific notation, please leave it in scientific notation rounded to one place after the decimal $($i$.$e$.,1\mathrm{.}210-4.$

It is believed to be true that $15\%$ of the U$.$S$.$ population is lefthanded. You randomly select eight people. Let $x$ represent the number of left$-$handers.

a$.$ Construct a binomial distribution using your graphing calculator.

b$.$ Find the probability that exactly $6$ people are left$-$handed.

c$.$ Find the probability that less than $3$ people are left$-$handed.

d$.$ Find the probability that at least $1$ person is left$-$handed.

e$.$ Find the mean of the binomial distribution.

f$.$ Find the standard deviation of the binomial distribution.

Complete the following sentence:

a$.$ In our SCC class data, we surveyed a TOTAL $($combine male sample data and female sample data$)$ of

$(n)$ students and found that

$($x$)$ of those surveyed were left$-$handed.

b$.$ Assuming that $15\%$ of the population is left$-$handed, find the probability of surveying $n$ students and getting exactly $x$ "lefties" $($Use the numeric values for $n$ and $x$ from our SCC class data.$)$

c$.$ In chapter $3,$ we noted that an event that occurs with a probability of $0\mathrm{.}05$ or less is considered unusual. Is the number of "lefties" $($x$)$ in our data unusual? $($State yes or no$)$

d$.$ Assuming that $15\%$ of the population is left$-$handed and we surveyed a total of $(n)$ students, calculate the mean.

e$.$ Using the mean from part $d,$ should we have expected more or less "lefties" in our SCC class data?