### Calculate the variance and the standard deviation of this binomial distribution.

Data Analytics

**S M 9115 Data Analytics for Decision Making 2**

**Problem 1 (35 pts)****
**A hotel manager wants to analyze the nationality of the guests who stayed at the hotel during the last month. The data shows that approximately 20% of the guests were from Germany. Suppose that you choose randomly 50 guests:

- Find the probability that exactly 10 guests are from Germany.

2. Find the probability that at least 15 guests are from Germany.

3. Find the probability that at most 5 guests are from Germany.

4. Find the probability that more than 30 guests are from Germany.

5. What is the expected number of guests from Germany who stayed at the hotel during the last month?

6. Calculate the variance and the standard deviation of this binomial distribution.

**Problem 2 (35 pts)****
**The manager of a hotel chain is interested in knowing whether there is a relationship between the number of positive reviews a hotel receives online and its occupancy rate. The manager collected data from 10 hotels and recorded the number of positive reviews each hotel received on a popular travel website and the corresponding occupancy rate (in percentage) for the same period. The data is shown below:

Hotel Positive Reviews Occupancy Rate%

45 72

65 82

55 78

80 89

75 86

70 81

90 92

50 76

60 77

85 88

- Determine the dependent and independent variables.

2. Calculate the correlation coefficient and comment.

3. Determine the regression equation 𝑌̂ = 𝑎 + 𝑏𝑋.

4. Give a brief interpretation for the values of “a” and “b”.

5. If the hotel had no positive reviews, what would the occupancy rate be?

**Problem 3 (30 pts)****
**The revenue manager of a hotel chain wants to analyze the distribution of room rates for a particular hotel location. Based on historical data, she estimates the following probability distribution for the daily room rates:

Probability Room Rate

30% $100

40% $150

20% $200

5% $250

5% $300

Based on this distribution, what is the coefficient of variation for the room rates at this hotel location?