Question

Allegiant Airlines charges a mean base fare of $89. In addition, the airline charges for making a reservation on its website, checking bags, and inflight beverages. These additional charges average $39 per passenger. Suppose a random sample of 50 passengers is taken to determine the total cost of their flight on Allegiant Airlines. The population standard deviation of total flight cost is known to be $36. Use z-table.

a. What is the population mean cost per flight? $

b. What is the probability the sample mean will be within $10 of the population mean cost per flight (to 4 decimals)? c.

c.What is the probability the sample mean will be within $5 of the population mean cost per flight (to 4 decimals)?

Answer 1

(a)

Population mean = = 89 + 39 = 128

(b)

Given:

Population SD = = 36

n = Sample size = 50

SE = /

= 36/ = 5.0911

Sample mean within 10 of population mean:

Z = 10/5.0911 = 1.9642

Table of Area Under Standard Normal Curve gives area = 0.4750

So,

Sample mean within 10 of population mean = 0.4750 X 2 = 0.9500

(c)

Sample mean within 5 of population mean:

Z = 5/5.0911= 0.9812

Table gives area = 0.3365

So,

Sample mean within 5 of population mean = 0.3365 X 2 = 0.6730