Question

tim worker is doing his budget. he discovers that the average electric bill for the year was $206.00 with a standard deviation of $10.00. what percent of his expenses in this category would he expect to fall between $184.00 and $200.00? the z for $184.00 = the percent of area associated with $184.00 = % the z for $200.00 = the percent of area associated with $200.00 = % subtracting the two percentages, the percent of expenses between $184.00 and $200.00 is %

Explanation:

Step1: Calculate z - score formula

The z - score formula is $z=\frac{x - \mu}{\sigma}$, where $x$ is the value, $\mu$ is the mean, and $\sigma$ is the standard deviation. Given $\mu = 206$, $\sigma=10$.

Step2: Calculate z - score for $x = 184$

$z_1=\frac{184 - 206}{10}=\frac{- 22}{10}=-2.2$

Step3: Find area for $z=-2.2$

Looking up in the standard - normal distribution table, the area to the left of $z = - 2.2$ is approximately $0.0139$ or $1.39\%$.

Step4: Calculate z - score for $x = 200$

$z_2=\frac{200 - 206}{10}=\frac{-6}{10}=-0.6$

Step5: Find area for $z=-0.6$

Looking up in the standard - normal distribution table, the area to the left of $z=-0.6$ is approximately $0.2743$ or $27.43\%$.

Step6: Calculate the percentage between 184 and 200

The percentage of expenses between $184$ and $200$ is $27.43\%-1.39\% = 26.04\%$

Answer:

$26.04$