USE THE INFORMATION BELOW TO ANSWER QUESTIONS $19$ THRU $21$

The Natural Resources Defense Council $($NDRC$)$ is a large organization dedicated to safeguarding people, plants and animals on the earth. They work to support clean air, clean water and healthy communities with an emphasis on pointing out water concerns in communities across the planet. Flint, Michigan has a known problem with an excess of lead in their drinking water which is very harmful to the health of the people in the community, especially children. The blood lead level in children in Flint during the peak of the water crisis $(2015)$ is known to be approximately normally distributed with a mean of $1\mathrm{.}31$ micrograms per deciliter $($ mpd $)$ with a standard deviation of $0\mathrm{.}030$ micrograms per deciliter. Assume that our interest is in probabilities about the blood lead level of a random child in Flint in the year $2015.$

$19.$ Pick the equation most appropriate to deal with the problem above.

a$)p(x)=(nCx)p^x(1-p{)}^{n-x}$

b$)z=\frac{(\stackrel{}{x})-}{\frac{}{\sqrt[\phantom{2}]{n}}}$

c$)\stackrel{}{x}+-z(\frac{s}{\sqrt[\phantom{2}]{n}})$

d$)z=\frac{x-}{}$

$20.$ What is the probability that a random child in Flint during $2015$ had a blood lead level in excess of $1\mathrm{.}39$ mpd $?$

a$)0\mathrm{.}0084$

b$)0\mathrm{.}0038$

c$)0\mathrm{.}0639$

d$)0\mathrm{.}0451$

$21.$ Select the value $($rounded to two decimal places$)$ that corresponds to the $70$ th percentile of this distribution. Note: Recall that, for example, the $65$th percentile corresponds to the value of blood lead level where $65\%$ of the distribution is below that particular value.

a$)1\mathrm{.}35$ mpd

b$)1\mathrm{.}33$ mpd

c$)1\mathrm{.}29$ mpd

d$)1\mathrm{.}31$ mpd

USE THE INFORMATION BELOW TO ANSWER QUESTIONS $22$ THRU $23$

In recent years home lighting technology has changed dramatically due to the development of Light Emitting Diode $($LED $)$ bulbs. Although previously used mainly in traffic lights and although LED bulbs are more expensive than incandescent bulbs, they use approximately $90\%$ less energy and they last up to $25$ times longer than incandescent bulbs. It has been estimated that the average home saves $$250$ per year using LED bulbs rather than incandescent bulbs. One popular manufacturer of LED bulbs claim that nearly all of their $75-$watt LEDs will last for more than $25,000$ hours.

$22.$ Suppose that a small company purchases $200$ of these $75-$watt LEDs with a guarantee that $95\%$ of them will last for more than $25,000$ hours. Assuming the guarantee is correct, what is the probability that at least $190$ of them will last for more than $25,000$ hours?

a$)0\mathrm{.}5831$

b$)0\mathrm{.}6823$

c$)0\mathrm{.}5293$

d$)0\mathrm{.}5631$

$23.$ Suppose that a small company purchases $350$ of these $75-$watt LEDs with a guarantee that $98\%$ of them will last for more than $25,000$ hours. Assuming the guarantee is correct, what is the expected number of them that will last for more than $25,000$ hours?

a$)345$

b$)340$

c$)343$

d$)336$

$7$