Question

please answer all parts.

Since 1900, the magnitude of earthquakes in California is approximately normally distributed with a mean of 6.21 and a standard deviation of 0.85, according to data obtained from the United States Geological Survey. a. What is the probability a randomly selected California earthquake has a magnitude of 6.9 or greater? o probability b. Earthquakes in the top 17% are categorized as severe. What magnitude corresponds to a severe earthquake magnitude-

Answer 1

Solution:-

Mean = 6.21, S.D = 0.85

a) The probability a randomly selected California earthquake has a magnitude of 6.9 or greater is 0.208.

x = 6.9

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

z = 0.812

P(z > 0.812) = 0.208

b) The magnitude corresponding to severe earthquake is 7.021.

p-value for the top 17% = 1 - 0.17 = 0.83

z-score for the p-value = 0.954

By applying normal distribution:-

$z = \frac{x-\mu }{\sigma }$

x = 7.021