Question

A radar unit is used to measure speeds of cars on a miter way the speed are normally distributed with a mean of 90 km/hr and a standard deviation of 10 km/hr what is the probability that’s a car picked at random is traveling at more than 100 km/hr

Answer 1

Using the normal distribution, there is a 0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

Normal Probability Distribution

The z-score of a measure X of a normally distributed variable with mean $\mu$ and standard deviation $\sigma$ is given by:

$Z = \frac{X - \mu}{\sigma}$

• The z-score measures how many standard deviations the measure is above or below the mean.

• Looking at the z-score table, the p-value associated with this z-score is found, which is the percentile of X.

The mean and the standard deviation are given, respectively, by:

$\mu = 90, \sigma = 10$

The probability that’s a car picked at random is traveling at more than 100 km/hr is one subtracted by the p-value of Z when X = 100, hence:

$Z = \frac{X - \mu}{\sigma}$

$Z = \frac{100 - 90}{10}$

Z = 1

Z = 1 has a p-value of 0.8413.

1 - 0.8413 = 0.1587.

0.1587 = 15.87% probability that’s a car picked at random is traveling at more than 100 km/hr.

More can be learned about the normal distribution at brainly.com/question/28096232

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