Answer:
Step-by-step explanation:
Since the amounts of charges are assumed to be normally distributed,
we would apply the formula for normal distribution which is expressed as
z = (x - µ)/σ
Where
x = the amounts of charges.
µ = mean amount
σ = standard deviation
From the information given,
µ = $500
σ = $80
a) the probability that customers charges more than $380 per month is expressed as
P(x > 380) = 1 - P(x ≤ 380)
For x = 380,
z = (380 - 500)/80 = - 1.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.067
P(x > 380) = 1 - 0.067 = 0.933
The percentage of customers that charges more than $380 per month is
0.933 × 100 = 93.3%
b) the probability that customers charges less than $340 per month is expressed as
P(x < 340)
For x = 340,
z = (340 - 500)/80 = - 2
Looking at the normal distribution table, the probability corresponding to the z score is 0.023
The percentage of customers that charges less than $340 per month is
0.023 × 100 = 2.3%
c) the probability that customers charges between $644 and $700 per month is expressed as
P(644 ≤ x ≤ 700)
For x = 644,
z = (644 - 500)/80 = 1.8
Looking at the normal distribution table, the probability corresponding to the z score is 0.96
For x = 700,
z = (700 - 500)/80 = 2.5
Looking at the normal distribution table, the probability corresponding to the z score is 0.994
P(644 ≤ x ≤ 700) = 0.994 - 0.96 = 0.034
The percentage of customers that charges between $644 and $700 per month is
0.034 × 100 = 3.4%
