Question

The average apartment rental at Gotham is approximately $615 per month. Suppose these rates are roughly normal with a standard deviation of $100. What proportion of rentals:

1. is at least $710 per month?    

2. is less than $450 per month?   

3. is between $450 and $800 per month?   

Use the Z-score table of Areas Under the Standardized Normal Distribution. You may find it in Appendix D of the Basic Econometrics textbook.

Please round your Z score to the nearest Z table value. For example, round Z=1.2345 to Z=1.23.

Answer 1

This is a normal distribution question with

1) P(x > 710.0)=?
The z-score at x = 710.0 is,

z = 0.95
This implies that
P(x > 710.0) = P(z > 0.95) = 1 - 0.8389
P(x > 710.0) = 0.1711
2) P(x < 450.0)=?
The z-score at x = 450.0 is,

z = -1.65
This implies that
P(x < 450.0) = P(z < -1.65) = 0.0495
3) P(450.0 < x < 800.0)=?

This implies that
P(450.0 < x < 800.0) = P(-1.65 < z < 1.85) = P(Z < 1.85) - P(Z < -1.65)
P(450.0 < x < 800.0) = 0.9678 - 0.0495
P(450.0 < x < 800.0) = 0.9184
PS: you have to refer z score table to find the final probabilities.
Please hit thumps up if the answer helped you