The scores of fourth grade students on a mathematics achievement test follow a normal distribution with a mean of 75 and standard deviation of 4. What is the probability the sample mean score of 64 randomly selected students is between 74 and 76?
Solution :
Given that,
mean = = 75
standard deviation = = 4
n=64
_{} = 75
_{} = / n = 4 / 64=0.5
= P(74< <76 ) = P[(74 - 75) /0.5 < ( - _{} ) / < (76 - 75) / 0.5)]
= P(-2 < Z <2 )
= P(Z <2 ) - P(Z <-2 )
Using z table,
= 0.9772 -0.0228
= 0.9544
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