Question

3.4 ​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.

b.​The top 2.5% of the property crime rates are greater than what value?

c.​What percent of property crime rates are between 3331 and 5518?

Answer 1

b)

z value at 2.5% = 1.96

z = (x - mean)/(s/sqrt(n))

1.96 = (x - 3331)/(729/sqrt(24))

x = 3622.66

x = 3623 rounding to whole number

b)

Here, μ = 3331, σ = 148.806501874078, x1 = 3331 and x2 = 5518. We need to compute P(3331<= X <= 5518). The corresponding z-value is calculated using Central Limit Theorem

z = (x - μ)/σ
z1 = (3331 - 3331)/148.806501874078 = 0
z2 = (5518 - 3331)/148.806501874078 = 14.7

Therefore, we get
P(3331 <= X <= 5518) = P((5518 - 3331)/148.806501874078) <= z <= (5518 - 3331)/148.806501874078)
= P(0 <= z <= 14.7) = P(z <= 14.7) - P(z <= 0)
= 1 - 0.5
= 0.5