Question

suppose a simple random sample size n=49

Suppose a simple random sample of size n= 49 is obtained from a population with u = 82 and o = 28. (a) Describe the sampling distribution of x. (b) What is P (X> 86.2)? (c) What is P (572) (d) What is P (76<x< 88.6)? Click here to view the standard normal distribution table page) Click here to view the standard normal distribution table (page 2). (a) Choose the correct description of the shape of the sampling distribution of x. OA. The distribution is skewed left. OB. The distribution is skewed right nts OC. The distribution is uniform cess D. The distribution is approximately normal. Librai we S S . More Options Click to select your answer(s). ons Type here to search Copyright 2020 Pearson Education Inc. All rights reserved. Terms of Use / e O BE hp 2 10 # $ % 00 2 3 4 5 6 7 8 w E R T Y U

Answer 1

a) Answer: D) The distribution is approximately normal u b) P(X>86.2)=P( 86.2- g/vn g/vn = P(Z > 86.2-82 28/149 = P(Z >1.05) = P(O<Z<)- P(0<7<1.05) = 0.5 -0.3531 (from normal table) P (>86.2) = 0.1469 - c) P (<72)=PG <72-3 g/n/vn 72-82 =P(Z < w28/149 =P (Z<-2.5) = P(-0<Z<0) - P(-2.5<7<0) = 0.5 -0.4938 (from normal table) P(X<72) = 0.0062

76- X- d) P (76<<88.6) =P < 88.6-5 s/vn o/vñ o/vn 76-82 =PG 28/149 <Z 88.6-82 28/49 = P (-1.5<7<1.65) = P(-1.5<7<0) + P(0<Z<1.65) = 0.4332 +0.4505 (from normal table) P (76< X <88.6) = 0.8837