Light it up! The graph below is a cumulative relative frequency graph showing the lifetimes (in hours) of $200$ lamps.

(a) Estimate the ${60}^{th}$ percentile of this distribution. Show your method.

(b) What is the percentile for a lamp that lasted $900$ hours?

On a scale of $100$, a score in the ${95}^{th}$ percentile represents the percentage of a distribution that is equal to or below it.

Step 1: Determine the place on the ogive where the line intersects the ogive by drawing a horizontal line from the value $60$ on the vertical axis.

Step 2: From this point, draw a vertical line to the horizontal axis. At around $1000$, the line intersects the axis. The 60th percentile of the lifespan of $2000$ bulbs is estimated to be $1000$ in the graph above. Therefore, $1000$ is the estimate of the ${60}^{th}$percentile of the lifetimes of $2000$ lamps.

Step 1: Determine the location on the ogive where the line intersects the ogive by drawing a vertical line from the value$900$ on the horizontal axis.

Step 2: From this point, draw a horizontal line to the vertical axis. At around $35$, the line crosses the axis. A light that lasts $900$ hours is in the ${35}^{th}$ percentile, according to the graph above.

Therefore, a lamp that lasted $900$ hours is at ${35}^{th}$ percentile.