amh926292
18.02.2020 •
Mathematics
Assume the speed of vehicles along the highway has an approximately normal distribution with a mean of 71 mph and a standard deviation of 8 mph.
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
b. What proportion of the vehicles would be going less than 50 mph?
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
Solved
Show answers
More tips
- C Computers and Internet How to easily and quickly disable Firebug in Gmail and Google Docs...
- G Goods and services How to sew a ribbon: Tips for beginners...
- F Food and Cooking How to Make Mayonnaise at Home? Secrets of Homemade Mayonnaise...
- C Computers and Internet Which Phone is Best for Internet Surfing?...
- F Food and Cooking Everything You Need to Know About Pasta...
- C Computers and Internet How to Choose a Monitor?...
- H Horoscopes, Magic, Divination Where Did Tarot Cards Come From?...
- S Style and Beauty How to Make Your Lips Fuller? Ideas and Tips for Beautiful Lips...
- C Computers and Internet How to Learn to Type Fast?...
Answers on questions: Mathematics
- M Mathematics An astronaut s pack weighs 18. 5 n when she is on earth but only 3. 84 n when she is at the surface of moon....
- M Mathematics Max has more than 5 carrots inequality...
- M Mathematics Pls answer the image below ...
- C Chemistry Looking at the reaction N2 + O2 → 2NO at 25°C, AH = +1.81 KJmol. Wh.at will be if the system is cooled? (A) The equilibrium will shift to the right (B) the system...
- M Mathematics The figure below shows a triangular piece of cloth: Triangle ABC has angle ABC equal to 90 degrees and angle BAC equal to 38 degrees. Length of AC is 5 inches. What...
- B Biology Plz help me with this question! What part of cell division do cells spend most time?...
Ответ:
a) 22.66% of vehicles are less than or equal to the speed limit
b) So 0.47% of the vehicles would be going less than 50 mph
c) The new speed limit will be 81.24 mph.
Step-by-step explanation:
Problems of normally distributed samples are solved using the z-score formula.
In a set with mean and standard deviation , the zscore of a measure X is given by:
The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.
In this problem, we have that:
a. The current speed limit is 65 mph. What is the proportion of vehicles less than or equal to the speed limit?
This is the pvalue of Z when X = 65. So
has a pvalue of 0.2266.
So 22.66% of vehicles are less than or equal to the speed limit
b. What proportion of the vehicles would be going less than 50 mph?
This is the pvalue of Z when X = 50. So
has a pvalue of 0.0047.
So 0.47% of the vehicles would be going less than 50 mph
c. A new speed limit will be initiated such that approximately 10% of vehicles will be over the speed limit. What is the new speed limit based on this criterion?
This is the value of X when Z has a pvalue of 1-0.1 = 0.9. So it is X when
Ответ:
same as 25(10/4)