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In: Statistics and Probability

A Gaussian random voltage has a mean of 4 and a variance of 10. a.) What...

A Gaussian random voltage has a mean of 4 and a variance of 10.

a.) What is the probability than an observed value of the voltage is greater than zero?

b.) What is the probability than an observed value of the voltage is greater than zero but less than or equal to the mean value?

c.) What is the probability that an observed value of the voltage is greater than twice the mean value?

Solutions

Expert Solution

Solution:

We are given

Therefore,

a.) What is the probability that an observed value of the voltage is greater than zero?

Answer:

We have to find:

The Z-score formula is:

  

Now using the standard normal table, we have:

Therefore, the probability that an observed value of the voltage is greater than zero is 0.8962

b.) What is the probability that an observed value of the voltage is greater than zero but less than or equal to the mean value?

Answer: We have to find:

The Z-score formula is:

When x = 0,

  

When x = 4.

  

Now using the standard normal table, we have:

  

  

Therefore, the probability that an observed value of the voltage is greater than zero but less than or equal to the mean value is 0.3962

c.) What is the probability that an observed value of the voltage is greater than twice the mean value?

Answer: We have to find:

The Z-score formula is:

  

Now using the standard normal table, we have:

Therefore, the probability that an observed value of the voltage is greater than twice the mean value is 0.1038

orchestra answered 2 years ago
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