3. Ames Homes. In 2015 a 3 bedroom home in Ames Iowa sold for an average of $136

Question

3. Ames Homes. In 2015 a 3 bedroom home in Ames Iowa sold for an average of $136 per square foot with a standard deviation of $22 per square foot. Further, prices per square foot in Ames IA are normally distributed. Use this information to answer the following questions. (a) What is the probability in 2015 that a 3 bedroom home in Ames Iowa sold for more than $152 per square foot? Answer this question by completing parts (i) and (ii). i. Provide the z-score corresponding to the above statement. ii. Use the z-score found in (i) to find the probability in 2015 that a 3 bedroom home in Ames Iowa sold for more than $152 per square foot? (b) What is the probability in 2015 that a 3 bedroom home in Ames Iowa sold for less than $127 per square foot? Answer this question by completing parts (i) and (ii). i. Provide the z-score corresponding to the above statement. ii. Use the z-score found in (i) to find the probability in 2015 that a 3 bedroom home in Ames Iowa sold for less than $127 per square foot? (c) Find Q1 (First Quartile). Answer this question by completing parts (i) and (ii). i. Provide the z-score corresponding to the above statement. ii. Use the z-score found in (i) to help you find the value of Q1. (Round answer to 3 decimal places.) (d) Find Q3 (Third Quartile). Answer this question by completing parts (i) and (ii). i. Provide the z-score corresponding to the above statement. ii. Use the z-score found in (i) to help you find the value of Q3. (Round answer to 3 decimal places.) (e) What is the value of the IQR for the distribution of 3 bedroom homes in Ames Iowa during 2015? (Round answer to 3 decimal places.) (f) What is the price per square foot such that only 4% of 3 bedroom homes in Ames Iowa sold for more than this amount in 2015? Answer this question by completing parts (i) and (ii). i. Provide the z-score corresponding to the above statement. ii. Use the z-score found in (i) to help you find the price per square foot such that only 4% of 3 bedroom homes in Ames Iowa sold for more than this amount in 2015? (Round answer to 2 decimal places.) iii. What percentile does the price per square foot obtained in part (ii) correspond to? (Enter value as a whole number, not a proportion.) (g) Free response submission. Which 3 bedroom home sold in Ames Iowa during 2015 is more unusual, a home with a sales price of $155 per square foot or a home with a sales price of $115 per square foot? Explain your answer

Explanation / Answer

3. Ames Homes. In 2015 a 3 bedroom home in Ames Iowa sold for an average of $136 per square foot with a standard deviation of $22 per square foot. Further, prices per square foot in Ames IA are normally distributed. Use this information to answer the following questions.

(a) What is the probability in 2015 that a 3 bedroom home in Ames Iowa sold for more than $152 per square foot? Answer this question by completing parts (i) and (ii).

i. Provide the z-score corresponding to the above statement.

Z=(152-136)/22 =0.73

ii. Use the z-score found in (i) to find the probability in 2015 that a 3 bedroom home in Ames Iowa sold for more than $152 per square foot?

P( x >152) = P( z > 0.73) = 0.2327

(b) What is the probability in 2015 that a 3 bedroom home in Ames Iowa sold for less than $127 per square foot? Answer this question by completing parts (i) and (ii).

i. Provide the z-score corresponding to the above statement.

Z=(127-136)/22 = -0.41

ii. Use the z-score found in (i) to find the probability in 2015 that a 3 bedroom home in Ames Iowa sold for less than $127 per square foot?

P( x <127) = P( z < -0.41) = 0.3409

(c) Find Q1 (First Quartile). Answer this question by completing parts (i) and (ii).

i. Provide the z-score corresponding to the above statement.

Z=-0.674

ii. Use the z-score found in (i) to help you find the value of Q1. (Round answer to 3 decimal places.)

Q1=136-0.674*22 = 121.172

(d) Find Q3 (Third Quartile). Answer this question by completing parts (i) and (ii).

Z=0.674

Q3 =136+0.674*22 =150.828

(e) What is the value of the IQR for the distribution of 3 bedroom homes in Ames Iowa during 2015? (Round answer to 3 decimal places.)

IQR = 150.828 - 121.172 = 29.656

(f) What is the price per square foot such that only 4% of 3 bedroom homes in Ames Iowa sold for more than this amount in 2015? Answer this question by completing parts (i) and (ii).

i. Provide the z-score corresponding to the above statement.

Z=1.751

X=136+1.751*22 = 174.522

X=174.52 ( rounded to two decimals)

Percentile = 96

(g) Free response submission. Which 3 bedroom home sold in Ames Iowa during 2015 is more unusual, a home with a sales price of $155 per square foot or a home with a sales price of $115 per square foot? Explain your answer

Z value for 155, z=(155-136)/22=0.86

Z value for 115, z=(115-136)/22=-0.95

Both are not unusual because both z values are within (-2, 2) z values.

Related Questions

Navigate

• Browse (All)
• Browse 3
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.