Question

The histogram below shows the responses of the 706 people from last semester to the Survey question: "What is the fastest you've ever driven? The average is about 90 mph and the SD is 15 mph.

The green lines indicate one SD above and below average and the blue lines indicate 2 SDs above and below average.

You can't use the graph above to answer the questions below, but you can use it to make sure your answers are in the right ballpark and make sense.

Since the histogram for speed is fairly close to bell shaped, we can use the normal approximation to estimate percentages. Use the normal curve to estimate what percent of the students have never driven over 97.5 mph. (For all normal approximation problems on homework and exams, unless told otherwise, you may round z scores to fit the closest line on the table and you may round percents on the table to the nearest whole number.)

So far you've been given the Value (speed) and asked to convert to a Z score and then find the appropriate area or percentile on the Normal Curve. The next question asks you to go in the opposite direction — you're given the percentile and you need to find the corresponding Z score (by breaking the histogram into a middle area and 2 tails so you can use the normal table) and then convert that z score to a value (speed) . (You may need to review pages 45-46 in the Notes.)

8. If someone is in the 40 th percentile (i.e., drove faster than 40 % of the class, what is the fastest (s)he ever drove?

First find the z score. (HINT: Note the relation between 40 th and 60 th percentiles. One is 10 % below and the other is 10 % above average, so think how the z score you just found for 60 th percentile relates to the z score you want here.)

9. Now change the z score for the 40 th percentile to a speed. ______MPH

Updated Layout

speed:15 speed : 100 n 80 60 40 20 200 150 100 50 -50 speed >=15 speed: 1. First, convert 97.5 mph to a z score. (average-90 mph,SD-15 mph.) mph Submit Answer Tries 0/5 2. Now use the normal table to find the middle area corresponding to the z score you just got. Submit Answer Tries 0/5 3. Finally, what percent of the histogram is above 97.5 mph? Again, check the graph to make sure your answer looks right. Be sure to read rounding instructions at the top of Submit Answer Tries 0/5 4. Use the normal approximation to calculate what percent of the class listed fastest speeds between 99 mph and 114 mph. First, convert 99 mph and 114 mph to a z scores. 99 mph is a z score of: 114 mph is a z score of: Submit Answer Tries 0/s 5. Now use the normal table to find the area between those two z scores for 99 mph and 114 mph: Submit Answer Tries 0/5 6. What percentile is 99 mph? (This is the same as asking what percent of the data falls below 99 mph.) First, convert 99 mph to a z score Now use the normal table to find the middle area corresponding to the z score you just got. Now figure out all the area below 99 mph (that's the middle area plus the left tail) th percentile 7. If someone is in the 60 th percentile (i.e., drove faster than 60 % of the class), what is the fastest (s)he ever drove? Do this in 3 parts: i) What middle area should you look up on the table to find a Z score for 60 th percentile? Submit Answer Tries 0/4 i) Next, find the z score, corresponding to the middle area: Submit Answer Tries 0/4 iii)Now, change the z score to a speed mph

Answer 1

X 5-6 0-383 s0-3083 c(r :114396-16 Son 13.8 hP