# What is the probability that the area of the house would be at least 2100 square feet?

Key points to follow:

• Selling price in AED, the current price of the home evaluated by a professional.
• Size of the home in square feet: the total area of the house (including the garage, pool, etc.)
• Number of bedrooms: the no. of rooms in the house.
• No. of bathrooms: the no. of bathrooms in the house.
• Garage: 1 if the house has garage .zero if not. (1 = yes, 0 = no)
• Pool: 1 if the house has pool .zero if not. (1 = yes, 0 = no)
• Distance: the distance in Km between the HCT ADWC campus and the house.
• Location: the region in which the house is located
o 1: Abu Dhabi City
o 2: Khalifa city
o 3.Shahama
o 4.Bani Yas
o 5.Bahia

Refer to the data given by your teacher complete the following tasks.

TASK 1 – Chapter 5 (A Survey of Probability Concepts)

Construct a contingency table as given below to answer the following questions: 2 marks

Location
1(AD) 2(Khalifa) 3(Shahama) 4(Bani Yas) 5(Bahia)
Has Garage
Has No Garage

1. What approach of probability did you use? 1 mark
2. What is the probability of selecting a home with Garage? 1 mark
3. Find the probability of selecting a home in Bani Yas? 1 mark
4. Calculate the probability of selecting a home in Khalifa and has Garage? 1 mark
5. What is the probability of selecting a home in Bahia or has No Garage? 2marks

TASK 2-A – Chapter 6 (Probability Distribution)

1. Use column “number of bedrooms” to create a probability distribution. 2marks
2. Use your probability distribution to find the probability of selecting a home with more than 3
Bedrooms. 1 mark
3. Using the probability distribution table find the expected number of bedrooms. 2marks
4. Find the variance using the probability distribution. 2marks

TASK 2-B – Chapter 6 (Binomial Distribution)

5. Using MegaStat create a binomial distribution with n=60, p= probability of selecting a home with a pool and explain what does the chart show? 2marks
6. What are the expected number and the standard deviation of selecting a home with a pool? 2marks
7. What is the probability that all homes have a pool? 1mark
8. What is the percentage that fewer than 15 homes have a pool? 2marks
9. What is the probability that between 23 and 31 homes have a pool? 2marks

TASK 3: Chapter 7 (Continuous Probability Distributions)

1. Compute the mean and the standard deviation of the sales prices of the 60 homes. 2marks
2. What is the probability that the area of the house would be no more than 2,000 square feet? 2marks
3. What is the probability that the area of the house would be at least 2,100 square feet? 2marks
4. What is the probability that the area of the house would be between 2,200 square feet and 2,500 square feet? 2marks
5. About 68% of the areas of the houses fall between what two values? (Use Empirical rule) 2marks
6. Between what two area values does the middle 75% of homes (60 homes) fall? 2marks
7. What is the area of a house that separates the top 20% from the lower 80% of the 60 homes? 2marks

TASK 4: Chapter 8 (Sampling Methods)

1. Select a sample A of 16 homes from the 60 homes dataset then paste it into a new sheet and name it as (Sample A).

Use systematic method and mention the system that you have used. 2 marks
2. Select a sample B of 36 homes from the 60 homes dataset then paste it in a new sheet and name it as (Sample B). Use cluster method and explain. 2 marks
3. Compute the mean, the standard deviation and the standard error of the home prices of sample A. 2 marks
4. Compute the mean, the standard deviation and the standard error of the home prices of sample B. 1 mark
5. Compare answer 4) and 5). How can the sample error be reduced? 1 mark
6. What is the probability that the home prices of sample A would be less than AED 2,500,000? 2marks

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