Assume that police estimate that $30\%$ of drivers do not wear their seatbelts. They set up a safety$$ roadblock, stopping cars to check for seatbelt use. They stop $50$ cars during the first hour.

a$.$ Find the$$ mean, variance, and standard deviation of the number of drivers expected not to be wearing seatbelts. Use the fact that the mean of a geometric distribution is $\frac{1}{p}$

and the variance is ${}^2=\frac{q}{p^2}$

$.$

b$.$ How many cars do they expect to stop before finding a driver whose seatbelt is not$$ buckled?