In: Statistics and Probability
1. In 2007 the mean property crime rate (per 100,000) people for the 24 states west of the Mississippi River was 3331; the standard deviation was 729. Assume the distribution of crime rate is unimodal and symmetric.
A). The bottom 16% of the property crime rates are less than what value?
B) The top 2.5% of the property crime rates are greater than what value?
C) What percent of property crime rates are between 3391 and 5518?
Solution :
Given that,
mean = = 3331
standard deviation = = 729
A)
Using standard normal table,
P(Z < z) = 16%
P(Z < z) = 0.16
P(Z < -0.99) = 0.16
z = -0.99
Using z-score formula,
x = z * +
x = -0.99 * 729 + 3331 = 2609.29
Value = 2609.29
B)
Using standard normal table,
P(Z > z) = 2.5%
1 - P(Z < z) = 0.025
P(Z < z) = 1 - 0.025
P(Z < 1.96) = 0.975
z = 1.96
Using z-score formula,
x = z * +
x = 1.96 * 729 + 3331 = 4759.84
Value = 4759.84
C)
P(3391 < x < 5518) = P((3391 - 3331)/ 729) < (x - ) / < (5518 - 3331) / 729) )
= P(0.0823 < z < 3)
= P(z < 3) - P(z < 0.0823)
= 0.9987 - 0.5328
= 0.4659 = 46.59%
percent = 46.59%