The population mean and standard deviation are given below F

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.)

Solution

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