Question

question #15
for a population that is distributed normally with a mean of 25,413 and a standard deviation of 9,408,
calculate ( p(x>15,189) ).
.2593
.1133
.7407
.8614

Explanation:

Step1: Calculate the z - score

The formula for the z - score is \(z=\frac{X-\mu}{\sigma}\), where \(\mu = 25413\), \(\sigma=9408\), and \(X = 15189\).

$$ z=\frac{15189 - 25413}{9408}=\frac{- 10224}{9408}\approx - 1.09 $$

Step2: Find the probability using the standard normal distribution

We want to find \(P(X>15189)\), which is equivalent to \(P(Z>-1.09)\) using the standard normal transformation.
Since \(P(Z > z)=1 - P(Z\leq z)\), and from the standard normal table \(P(Z\leq - 1.09)=0.1379\)

$$ P(Z>-1.09)=1 - 0.1379 = 0.8621\approx0.8614 $$

(There may be some minor differences due to rounding in the standard - normal table values)

Answer:

\(0.8614\)