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Answer:
a) (<em>μ</em>) = $128
b) 0.9472
c) 0.6671
Step-by-step explanation:
Given that:
Allegiant Airlines charges a mean base fare of $89.
this implies that: mean base fare = $89.
The question proceeds by stating the additional charge on its website, checking bags, and inflight beverages.
so , additional charges turns out to be = $39 per passenger
Now, Suppose a random sample of 60 passengers is taken
random sample (n) = 60
The population standard deviation of total flight cost is known to be $40
standard deviation (σ) = 40
Question (a) says; we should find the population mean cost per flight
To determine that; we have to consider the total sum(<em>μ</em>) of the mean base fare with the mean additional charges.
Population mean cost per flight (<em>μ</em>) = mean base fare + mean additional charges
(<em>μ</em>) = $89 + $39
(<em>μ</em>) = $128
b)
What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)?
To determine that; we have:
P(128 - 10 ≤ Х ≤ 128 +10)
= P(118 ≤ Х ≤ 138)
= (where
= <em>μ </em>and ∝ = σ )
=
=
Using Excel Command to approach this process, we have;
= 0.9736 - 0.0264
= 0.9472 (to four decimal places)
∴ the probability that the sample mean will be within $10 of the population mean cost per flight = 0.9472
c)
What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?
We wll have to go through the process like the one attempted above in question (b);
So;
P(128 - 5 ≤ Х ≤ 128 + 5)
= P(123 ≤ Х ≤ 133)
= (where
= <em>μ </em>and ∝ = σ )
=
=
Computing these data in Excel; we have
= 0.8335 -0.1665
= 0.6671 (to 4 decimal places)
∴ the probability that the sample mean will be within $5 of the population mean cost per flight.