The population mean and standard deviation are given below. Find the required pr

Question

The population mean and standard deviation are given below. Find the required probability and determine whether the given sample mean would be considered unusual.

For a sample of

nequals=61,

find the probability of a sample mean being less than 22.5 if U=23 and sigmaequals=1.21

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For a sample of nequals=61,the probability of a sample mean being less than 22.5 if mu equals 23 and sigmaequals=1.21 is ?

(Round to four decimal places as needed.)

Explanation / Answer

Normal Distribution
Mean ( u ) =23
Standard Deviation ( sd )=1.21
Normal Distribution = Z= X- u / sd ~ N(0,1)                  
P(X < 22.5) = (22.5-23)/1.21/ Sqrt ( 61 )
= -0.5/0.1549= -3.2274
= P ( Z <-3.2274) From Standard NOrmal Table
= 0.0006                  

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