Question

5.2 The Uniform Distribution Use the following information to answer the next ten questions. The data that follow are the square footage (in 1,000 feet squared) of 28 homes. 1.5 2.4 3.6 2.6 1.6 2.4 2.0 3.5 2.5 1.8 2.4 2.5 3.5 4.0 2.6 1.6 2.2 1.8 3.8 2.5 1.5 | Table 5.4 CHAPTER 5 CONTINUOUS RANDOM VARIABLES 325 2.8 1.8 4.5 1.9 1.9 3.1 1.6 Table 5.4 The sample mean = 2.50 and the sample standard deviation = 0.8302. The distribution can be written as X U(1.5, 4.5). i What type of distribution is this? i What is the height of f(x) for the continuous probability distribution? iï Graph P(2<x<3). iv What is P(x<3.5|x < 4)? v What is the 90th percentile of square footage for homes?

Answer 1

classmate Date Page - solution : dle have, - Xoves, 4.5), d21:51 b-4.5 x=2.50 / 1s=0.8302 Continuous (I) It is a uniform distribution because all Sample values uniformly distributed between 1.5 to 4.5. It is a continuous probability distribution. (II) The height of the Uniform distribution is t = - b-a = 4.5-is = - 2 plaLx 230 on 1.5 2 2.5 3 3.5 4.5 iv) The shaded region is equal to p(2<x<3) P(x<3:5 / x<4) - Rotxaw - PE X<3.5 0 8247 - P[X<4 P[X23.5 ] P[X<4 ]

classmate Date Page [3.5-1.57 +- 1.57 سایر di dla - 2.5 P ( X<3.5 / x <4) = 0.8 7 Now, goth pereentile is, . P[X<k] = Vzdx = 1/2 (k-1.5) = 0.90 Et = K-1.5 = 2.7 K -2.7 +1.5 k = 4:2 percentile - goth is 4.2.