Question

3 19. Given discrete uniform population f(x)= x-2,4,6 o otherwise Find probability thata random sample af 54 is selected with replacement will produce a sample mean greater than 4.1 but less than Assume means are measured to nearest 10th value

Answer 1

10 Let , x be the geondom Variable chaving below distribution, f(a 20 = 2, 4, 1. 3 0 otherwise So, meow cangu. E (x) = 2+1 3+ Axt, texta 4 + 56 3 & 1(x) = 2xy + y este ... Varianceo Elx?).-€" (*) 2 2 8 3 Now, we dravo, X, X2 2. .,X54. Sample from the above distribution the sample mean is, n I 51 54 54 Now, = E(X) = ME (7.) - E (54.3* 124 = 4 and o = Var(x) = Var (ta 3 Xi) Ivar(xi) 54² 54 8/3 54 4 81 By large sample (n=54) we can say, x att Normal (4 ; 1/2)

PC 4.1 - Hence, we need to find, < Ž < 4.4 4.4) P( 4.1-4 X - 4 4.4 - 4 ✓ / WA 4. 81 81 81 P( 0.45 < 3 < 1.8 $(18) - Z~N(0,1) standard Normal [20) CDF 042 $10.45 0.2904249 ( Amwer) CS

The nearest 10th value answer is 0.3

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