Question

Tim Worker is doing his budget. He discovers that the average electric bill for the year was $206 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 = -

.62.22


The percent of area associated with $184.00 =

62.2


The z for $200 = -

.622.22


The percent of area associated with $200 =

48.6


Subtracting the two percentages, the percent of expenses between $184.00 and $200.00 is

622.22


Thanking you in advance for your help.God bless you all

Answer 1

Answer:

• z for 184 = -2.2
• P(z < -2.2) ≈ 1.4%
• z for 200 = -0.6
• P(z < -0.6) ≈ 27.4%
• P(184 < x < 200) ≈ 26.0%

Step-by-step explanation:

Z is computed from ...

... z = (x -μ)/σ

Our lower limit for x is 184, so its z-value is ...

... z = (184 -206)/10 = -22/10 = -2.2

Our upper limit for x is 200, so its z-value is ...

... z = (200 -206)/10 = -6/10 = -0.6

A suitable table or probability calculator can tell you ...

... the percent of area associated with z = -2.2 is about 1.4%. That is, about 1.4% of all values lie below z = -2.2.

... the percent of area associated with z = -0.6 is about 27.4%.

The fraction of expenses between $184 and $200 is then calculated to be ...

... 27.4% - 1.4% = 26.0%