Answer:
a) 0.11277
b) 0.83253
c) 0.67364
Step-by-step explanation:
The formula for calculating a z-score is is z = (x-μ)/σ,
where x is the raw score
μ is the population mean
σ is the population standard deviation.
From the question,
Mean = $109.55.
Standard deviation = $21.00.
a) What proportion of bills are greater than $135?
z = (x-μ)/σ
z = 135 - 109.55/21
= 1.2119
Probability value from Z-Table:
P(x<135) = 0.88723
P(x>135) = 1 - P(x<135) = 0.11277
The proportion of bills are greater than $135 = 0.11277
(b) What proportion of bills are between $84 and $143?
For x = $84
z = (x-μ)/σ
z = 84 - 109.55/21
= -1.21667
Probability value from Z-Table:
P(x = 84) = 0.11187
For x = 143
z = (x-μ)/σ
z = 143 - 109.55/21
= 1.59286
Probability value from Z-Table:
P(x = 143) = 0.9444
The proportion of bills are between $84 and $143
= P(x = $143) - P(x = 84)
= 0.9444 - 0.11187
= 0.83253
(c) What is the probability that a randomly selected household had a monthly bill less than $119?
For x = $119
=119 - 109.55/ 21
= 0.45
Probability value from Z-Table:
P(x<119) = 0.67364
The probability that a randomly selected household had a monthly bill less than $119 is 0.67364
