Given,
Sample mean = ±3 of true mean
Standard error = 1.8
Therefore,
Required probability of sample mean being within 3 units of the true mean is,
P ( sample mean - 3 < mean < sample mean + 3 )
= P [( sample mean - 3 ) - mean / 1.8 ] < mean - sample mean / 1.8 < [ ( sample mean + 3 ) - mean / 1.8 ]
= P ( - 1.67 < ∉ < 1.67)
= P (∉ < 1.67) - P( ∉ < 1.67)
= 0.952 - 0.047
= 0.905
Hence, the probability that the sample mean is within 3 units of the true mean if the standard error is 1.8 is 0.905.
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