Answer to Question #139430 in Statistics and Probability for Archana jha

Question

The annual rainfall at a certain locality is known to

be normally distributed random variable with

mean value equal to 29.5 inches and standard

deviation of 2.5 inches. How many inches of rain

(annually) exceeded about 5% of time.​

Answer 1

Solution:

According to the Z-tables, the сut-off value of 0.95 corresponds to the Z-score $Z=1.645$

Z-score is calculated as:

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

Therefore:

$X=Z\times\sigma+\mu=1.645\times2.5\,inches+29.5\,inches=33.6125\,inches$

Answer:

33.6125 inches