A Population follows a normal distribution with mean 10 and standard deviation 2. In a sample of 100, what is the probability of the sample mean being between 9.5 and 10.1?

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Answer 1 · 2017-01-19T06:02:04

Probability of the sample mean being between 9.5 and 10.1#=0.5859 # or 90%

Given -

Population Mean #= 100#
Population Standard Deviation#=2#

Standard Error #=sigma/sqrtn=2/sqrt100=2/10=0.2#

Find #z# for #mu=9.5, mu=10.5#

#z=(mu -mu_(barx))/(SE)#

At #x=9.5; z = (9.5-10)/0.2=(-0.5)/0.2=-1.25#
At #x=9.5; z = (10.1-10)/0.2=(0.1)/0.2=0.5#
Area between #z=-0.25 and z= 0.05=0.3944 +0.01915=0.5859#

Probability of the sample mean being between 9.5 and 10.1#=0.5859 # or 90%

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