Question

step 3: apply the rule & report the final proportion
the average starting salary is μ = $49,000 and σ = $9,000. ? question: what is the final proportion of salaries between $30,000 and $70,000?
proportion within a range

1. calculate the z - scores for both $30,000 and $70,000
2. then use the z - table to find the two proportions.
3. subtract the proportions (z2 - z1) to find the proportion between them.

select the correct final proportion between from the options below.
p(z_final)=.0250
p(z_final)=.0273
p(z_final)=.9750
p(z_final)=.9727

Explanation:

Step1: Calculate z - score for $30,000

The formula for the z - score is $z=\frac{x-\mu}{\sigma}$. Here, $x = 30000$, $\mu=49000$, and $\sigma = 9000$. So, $z_1=\frac{30000 - 49000}{9000}=\frac{- 19000}{9000}\approx - 2.11$.

Step2: Calculate z - score for $70,000

Using the same formula, with $x = 70000$, $\mu=49000$, and $\sigma = 9000$. So, $z_2=\frac{70000 - 49000}{9000}=\frac{21000}{9000}\approx2.33$.

Step3: Find proportions from z - table

From the standard normal distribution table, the proportion corresponding to $z_1=-2.11$ is $P(Z < - 2.11)=0.0174$. The proportion corresponding to $z_2 = 2.33$ is $P(Z < 2.33)=0.9901$.

Step4: Calculate proportion between the two values

The proportion between $z_1$ and $z_2$ is $P(-2.11

Answer:

$p(z_{final}) = 0.9727$