Question

Z Scores and Probability: Suppose you are a researcher interested in studying international trade patterns and conflict. You collect information on the number of trade disputes each country was involved for 144 countries in 2011. The mean number of trade disputes was 25 with a standard deviation of 12 disputes. a.) Suppose the United States was involved in 42 international trade disputes in 2011. Find the Z- score for the United States in 2011, and report the probability that any country selected at random would have a Z-score higher than that of the United States. b.) You want to take a deeper look at those countries heavily involved in trade disputes, and choose to study the countries in the top ten percent of disputes. Find the minimum number of disputes that a country must have to meet this threshold.

Answer 1

Solution :

Given that ,

mean = = 25

standard deviation = = 12

a) x = 42

Using z-score formula,

z = x - /   

z = 42 - 25 / 12

z = 1.42

=P( z > 1.42)

=1- P(z < 1.42)

Using z table,

= 1 - 0.9222

= 0.0778

b) Using standard normal table,

P(Z > z) = 10%

= 1 - P(Z < z) = 0.10  

= P(Z < z) = 1 - 0.10

= P(Z < z ) = 0.90

= P(Z < 1.282 ) = 0.90  

z = 1.282

Using z-score formula,

x = z * +

x = 1.282 * 12 + 25

x = 40.38