Question

In: Statistics and Probability

A radar unit is used to measure speeds of cars on a motorway. The speeds are...

A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with LaTeX: \mu=90 μ = 90 km/hr and a standard deviation of LaTeX: \sigma=9.2 σ = 9.2 km/hr. Approximately 86.21% of the population has a speed of at least 100 km/hr. True or false?

Solutions

Expert Solution

Solution:

Given: The speeds are normally distributed with μ = 90 km/hr and a standard deviation of σ = 9.2 km/hr.

Statement: Approximately 86.21% of the population has a speed of at least 100 km/hr.

That is :

Since x = 100 is above mean value = μ = 90 km/hr, so probability of the population has a speed of at least 100 km/hr is less than 50%, that is probability speed is 100 or more is less than 50%

thus given statement is False.

We can verify by using following steps:

Find:

Find z score for x = 100

thus we get:

Look in z table for z = 1.0 and 0.09 and find corresponding area.

P( Z < 1.09) =0.8621

thus

Thus we have shown that the population has a speed of at least 100 km/hr is not 86.21%.

Thus given statement is False.

orchestra answered 1 year ago

Next > < Previous

Related Solutions

A radar unit is used to measure the speed of cars on a highway during rush...

A radar unit is used to measure the speed of cars on a highway during rush hour traffic. The speeds of individual cars are normally distributed with a mean of 55 mph and a standard deviation of 3.2 mph. Find the probability of the following events: (a) A car traveling faster than average. (b) A car traveling over 65 mph (c) A car traveling between 48 and 50 mph.

Please show your answer and a draw the graphs. A radar unit is used to measure...

Please show your answer and a draw the graphs. A radar unit is used to measure speeds of cars on a motorway. The speeds are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr. What is the probability that a car picked at random is travelling at more than 100 km/hr? For a certain type of computers, the length of time bewteen charges of the battery is normally distributed with a mean of 50...

assume the radar signals of 10 GHz are used to measure the rotation rates of Mercury...

assume the radar signals of 10 GHz are used to measure the rotation rates of Mercury and Venus. Using the Dopper effect, determine the relative shifts in frequency for signals returning from the approaching and receding limbs of each plant. Answers are 101 Hz and 60.4 Hz - need to show the work though.

Assume that the speeds of cars travelling on a stretch of highway are normally distributed. A...

Assume that the speeds of cars travelling on a stretch of highway are normally distributed. A sample of 25 cars on this highway found a mean speed of 70 mph with a standard deviation of 6 mph. Construct a 95% confidence interval for the true mean speed of all cars travelling on this stretch of highway. (need check the assumptions) What is the margin of error in (1). Interpret the 95% confidence interval in the context of the problem.

2. Speeds of the fastest cars at a race location are normally distributed with a mean...

2. Speeds of the fastest cars at a race location are normally distributed with a mean of 64.8 mph, and standard deviation 8.9 mph. Find the speed that separates the slowest 6% of vehicles from the rest. Round your answer to two decimal places. 3. Refrigerators of a certain type have lifetimes that are normally distributed with mean 675 hours and standard deviation 44.5 hours. Find the lifetime (in hours) that would separate the longest 1.5% from the rest. Round...

California Speeding: Listed below are the recorded speeds (in mi/hr) of randomly selected cars traveling on...

California Speeding: Listed below are the recorded speeds (in mi/hr) of randomly selected cars traveling on a section of Highway 405 in Los Angeles. That part of the highway has a posted speed limit of 65 mi/hr. Assume the standard deviation of speeds is 5.7 mi/hr. Use a 1% significance level to test the claim that sample is from a population with a mean weight that is greater than 65 mi/hr. 68 68 72 73 65 74 73 72 68...

A used car lot has 150 cars, 90 of the cars are black and 60 cars...

A used car lot has 150 cars, 90 of the cars are black and 60 cars are blue. What is the probability of 2 blue cars being test drove back to back; assuming the first car is purchased? What is the probability of 2 blue cars being test drove back to back; assuming the first car was not purchased?