Question

In: Statistics and Probability

1. In 2007 the mean property crime rate (per 100,000) people for the 24 states west...

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?

Solutions

Expert Solution

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%


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