Solution :
Given that,
mean =
= 62.6
standard deviation =
= 73.4
n = 162
M
= 62.6
M
=
/
n = 73.4 /
162 = 5.7668
P(48.2 < M < 67.8) = P((48.2 - 62.6 - 182.5) / 5.7668 <
(M -
M) /
M < (67.8 - 62.6) / 5.7668))
= P(-2.497 < Z < 0.902)
= P(Z < 0.902) - P(Z < -2.497)
= 0.8165 - 0.0063
= 0.8102
P(48.2 < M < 67.8) = 0.8102
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