5. You have measured the speed of exactly 400 randomly chosen vehicles and found

Question

5. You have measured the speed of exactly 400 randomly chosen vehicles and found that your estimated average speed between 3 pm and 4 pm is 52.32 mph and that your sample standard deviation is estimated to be 6.93 mph. The flow of vehicles at that time was 2,750 vph. Assume that vehicle speeds follow a Normal distribution and based on this and only this try to answer the following questions. (You may use textbook, notes, Internet, Excel spreadsheet, or the table on the back of this sheet as a help.) a) Estimate the 95%-ile speed at that time. Answer: 5% ofdrivers would go above: mph mph Estimate the 80%-ile speed at that time. Answer: 20% ofdrivers would go above Based on your study, what is the precision (also known as error) in mph of your estimate of the average speed with 95% level of confidence (That means that you are 95% confident that the estimated average value given above is no more than that much away from the true average, so use a two-tailed test value). Give answer with two decimals b) c)

Explanation / Answer

Sample 400 Population 2750 Sample mean speed 52.32 mph Sample std dev 6.93 mph a) 95 percentile speed Normal distribution with one tail test on right side Z = (Xbar - sample mean)/Sample stddev Z 1.645 Therefore Xbar = 63.71985 X critical for 95%ile is 63.7198 mph b) 80 percentile speed Normal distribution with one tail test on right side Z = (Xbar - sample mean)/Sample stddev Z 0.84 Therefore Xbar = 58.1412 X critical for 80%ile is 58.1412 mph c) 95% confidence interval two tailed test Z for 95% 1.96 Confidence level Min mean - Z*std dev 38.7372 mph Max mean + Z*std dev 65.9028 mph The 95% confidence interval for speed is (38.7372, 65.9028) mph

Related Questions

Navigate

• Browse (All)
• Browse 5
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.