Question

Math 333 ASAP please.

Suppose that X has a discrete uniform distribution f ( x ) = { 1 / 3, x = 1,2,3 0, otherwise A random sample of n = 34 is selected from this population. Find the probability that the sample mean is greater than 2.1 but less than 2.6. Express the final answer to four decimal places (e.g. 0.9876). The probability is Enter your answer in accordance to the question statement

Answer 1

x	P(X=x)	xP(x)	x2P(x)
1	0.333	0.33333	0.33333
2	0.333	0.66667	1.33333
3	0.333	1.00000	3.00000
total		2.0000	4.6667
	E(x) =μ=	ΣxP(x) =	2.0000
	E(x2) =	Σx2P(x) =	4.6667
	Var(x)=σ2 =	E(x2)-(E(x))2=	0.666667
	std deviation=	σ= √σ2 =	0.81650

for normal distribution z score =(X-μ)/σx

mean μ=	2
standard deviation σ=	0.8165
sample size       =n=	34
std error=σx̅=σ/√n=	0.1400

  probability that the sample mean is greater than 2.1 but less than 2.6:

probability =P(2.1<X<2.6)=P((2.1-2)/0.14)<Z<(2.6-2)/0.14)=P(0.71<Z<4.28)=1-0.7611=0.2389

(please try 0.2376 if this comes wrong and replty)_