Question

step 4: interpret the final proportion
the average starting salary is μ = $49,000 and σ = $9,000. what proportion of working recent college graduates will earn a salary within the interval of $30,000 to $70,000?
now that youve calculated the z - scores and found the area between them, its time to interpret the result.
? question: what does the proportion between $30,000 and $70,000 tell us about recent college graduates?
select the correct interpretation from the answer choices below.
the proportion of starting salaries within a range of $30,000 to $70,000, from a normal distribution with μ = $49,000 (σ = $9,000), is p =.9727.
the proportion of starting salaries outside a range of $30,000 to $70,000, from a normal distribution with μ = $49,000 (σ = $9,000), is p =.9772.
the proportion of starting salaries within a range of $30,000 to $70,000, from a normal distribution with μ = $49,000 (σ = $9,000), is p =.0273.
the proportion of starting salaries outside a range of $30,000 to $70,000, from a normal distribution with μ = $49,000 (σ = $9,000), is p =.0273.

Explanation:

The question asks for the interpretation of the proportion of starting - salaries within the range of $30,000 to $70,000 for a normal distribution with mean $\mu = 49000$ and standard deviation $\sigma=9000$. The proportion within the range is found by calculating the z - scores and the area between them. A high proportion within the range means most graduates' starting salaries fall in this interval.

Answer:

The proportion of starting salaries within a range of $30,000 to $70,000, from a normal distribution with $\mu = 49000$ ($\sigma = 9000$), is $p = 0.9727$.