Question

Assume that Richter scale magnitudes of earthquakes are normally distributed with a mean of 1.925 and a standard deviation of 0.317. Use the appropriate z-score table when necessary.

a.) What is the z score that corresponds to a Richter scale magnitude of 1.811? (round to two decimal places)

z = Answer

b.) What Richter scale magnitude (to three decimal places) would correspond to a z-score of 1.8?

Answer

c.) What is the probability of an earthquake having a Richter scale magnitude less than 1.811? (round to four decimal places)

probability = Answer

d.) What is the Richter scale magnitude that is associated to the bottom 1.2% of earthquakes. (round to three decimal places)

Answer

Answer 1

Solution :

Given that ,

mean = = 1.925

standard deviation = = 0.317

a.)

x = 1.811

z = x - / = 1.811 - 1.925 / 0.317 = -0.36

z = -0.36

b.)

x = 1.8

z = x - / = 1.8 - 1.925 / 0.317 = -0.394

Answer = -0.394

c.)

P(x < 1.811) = P[(x - ) / < (1.811 - 1.925) / 0.317]

= P(z < -0.36)

= 0.3594

Probability = 0.3594

d.)

Using standard normal table ,

P(Z < z) = 1.2%

P(Z < -2.26) = 0.012

z = -2.26

Using z-score formula,

x = z * +

x = -2.26 * 0.317 + 1.925 = 1.209

Answer = 1.209