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?

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 2 years ago

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