Question

The average daily rate of a hotel in Canada as of August 2018 was $ 193.75. Assume the average daily rate follows a normal distribution with a standard deviation of $ 24.70.

a. What is the probability that the average daily rate of a canadian hotel will be:
i) less than $170
ii) more than $210
iii) between $145 and $185

Answer 1

To find the probabilities, we calculate the z-scores for each value and use the standard normal distribution table.

Step-by-step explanation:

To find the probability in each scenario, we can use the standard normal distribution table or calculate the z-score and use the standard normal distribution. Let's calculate each scenario:

i) Less than $170:

To find the probability that the average daily rate is less than $170, we need to find the z-score for $170 using the formula: z = (x - μ) / σ. Plugging in the values, we get z = (170 - 193.75) / 24.70 = -0.96. Looking up the z-score in the standard normal distribution table, we find a probability of approximately 0.166.

ii) More than $210:

Similarly, to find the probability that the average daily rate is more than $210, we calculate the z-score: z = (210 - 193.75) / 24.70 = 0.66. Using the standard normal distribution table, we find a probability of approximately 0.254.

iii) Between $145 and $185:

To find the probability that the average daily rate is between $145 and $185, we calculate the z-scores for both values: z1 = (145 - 193.75) / 24.70 = -1.97 and z2 = (185 - 193.75) / 24.70 = -0.35. Using the standard normal distribution table, we find a probability of approximately 0.039 for z1 and 0.364 for z2. Subtracting the two probabilities, we get a probability of 0.364 - 0.039 = 0.325.