Question 1177992
P(x<981); z=(x-mean)/sd; 981-1002=-21
z < -21/278=-0.0755
probability is 0.4699
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sample mean <981 is z=(x bar-mean)/sigma/sqrt(n)
z < (-21)/278/sqrt(76)
=(-21/278)*(sqrt(76)/278=-0.6585
probability z < -0.6585=0.2551

Much less likely that the mean of a sample of 76 will be as small as 981 or less.
The fourth decimal place will change depending on the rules given for rounding z. If to two places, it will be different from the values here.