Answered: The average daily rate of a hotel in…

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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Question

The average daily rate of a hotel in Canada as of August 2018 was $193.65. Assume the average daily rate follows a normal distribution with a standard deviation of $24.60.

a. What is the probability that the average daily rate of a Canadian hotel will be:

(i) less than $170
P(X < 170)=

(ii) more than $200
P(X > 200)=

(iii) Between $145 and $185
P(145 < X < 185)=

b. Determine the average daily rates that separate the:

(i) top 8% of average daily rates from the rest of the daily rates or from the bottom 92% of average daily rates
x=

Round to 2 decimal places.

(ii) bottom 15% of average daily rates from the rest of the daily rates
x=

Round to 2 decimal places.

(iii) middle 70% of average daily rates from the rest of the daily rates

= ? < x < ?

Round to 2 decimal places.

Features Features Normal distribution is characterized by two parameters, mean (µ) and standard deviation (σ). When graphed, the mean represents the center of the bell curve and the graph is perfectly symmetric about the center. The mean, median, and mode are all equal for a normal distribution. The standard deviation measures the data's spread from the center. The higher the standard deviation, the more the data is spread out and the flatter the bell curve looks. Variance is another commonly used measure of the spread of the distribution and is equal to the square of the standard deviation.

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b. Determine the average daily rates that separate the:

(i) top 8% of average daily rates from the rest of the daily rates or from the bottom 92% of average daily rates
x=

Round to 2 decimal places.

(ii) bottom 15% of average daily rates from the rest of the daily rates
x=

Round to 2 decimal places.

(iii) middle 70% of average daily rates from the rest of the daily rates

= ? < x < ?

Round to 2 decimal places.

Solution