Question

The average daily rate of a hotel in Canada as of August 2018 was $183.75. Assume the average daily rate follows a normal distribution with a standard deviation of $21.80. Standard Normal Distribution Table a. What is the probability that the average daily rate of a Canadian hotel will be: (i) less than $165 P(X< 165) = (ii) more than $215 P(X>215) = 0 (iii) Between $155 and $195 P (155 < X < 195) = = 0 b. Determine the average daily rates that separate the: (i) top 3% of average daily rates from the rest of the daily rates or from the bottom 97% of average daily rates X = $0.00 Round to 2 decimal places. (ii) bottom 10% of average daily rates from the rest of the daily rates X = $0.00 Round to 2 decimal places. (iii) middle 65% of average daily rates from the rest of the daily rates $0.00 < x < $0.00 Round to 2 decimal places.

Answer 1

The student's task is to calculate probabilities and determine average daily rates in Canada using a normal distribution with a given mean and standard deviation, requiring understanding of Z-scores and standard normal distribution tables.

Step-by-step explanation:

The student's question involves using the properties of the normal distribution to calculate probabilities and determine specific values (average daily rates) associated with given percentages of the distribution. The average daily rate of a hotel follows a normal distribution, with a mean of $183.75 and a standard deviation of $21.80. To find the probabilities and the rates for different percentiles, we use the standard normal distribution (Z-score) formula and look up the corresponding probabilities in a Z-table.

Since no actual calculations were provided, we cannot suggest specific values. However, the process would involve finding the Z-scores for each scenario and then using those scores to find the probabilities from the standard normal table.