Question

The population mean and standard deviation are given below. Find the indicated probability and determine whether a sample mean in the given range below would be considered unusual. If convenient, use technology to find the probability, For a sample of n=33, find the probability of a sample mean being less than 12,751 or greater than 12,754 when = 12,751 and 6 =2.4. For the given sample, the probability of a sample mean being less than 12,751 or greater than 12,754 is (Round to four decimal places as needed.)

Answer 1

for normal distribution z score =(X-μ)/σx
here mean=       μ=	12751
std deviation   =σ=	2.400
sample size       =n=	33
std error=σx̅=σ/√n=	0.418

probability =1-P(12751<X<12754)=1-P((12751-12751)/0.418)<Z<(12754-12751)/0.418)=1-P(0<Z<7.18)=1-(1-0.5)=0.5000