Question

A simple random sample of size

n=49

is obtained from a population with

μ=73

and

σ=21.

​(a) Describe the sampling distribution of

x.

​(b) What is

P x>78.7​?

​(c) What is

P x≤66.25​?

​(d) What is

P 70.6<x<80.2​?

Answer 1

Giron na ug M=73 221 by Centre Limit Theorem (CLT) sampling distribution of it is normally distributed with mean (4x) and standard deviation (57) where elx = l = 73 and 21 Vug un XN Normal ( lx, 5x) when Z= X-1 N Normal 10, 1) 07

b] P ( x > 78.9) P I-lx > 78.7-73 plzs lig - I-plz<1.9) = -0.9013 = 10.0287 Answer i-0.0289 13) e] PC & <66.25) = P(Z< 66.25-73 - P(2<-2.25) = 1- P(Z <2.2) -0.9878 To.0122 Answer : 0.01221

3 a] P(70.6<$<80.2) = P(10.6=73 <75 80,2,-73 = P(-0.84252.4) p(z<2.4) -P(240.8) 8(2624)*P(2¢0.87] =P(2.82.4) -AP (2508) 0.9918-1+017881 E10.77991 Answer: 07 799)