Solution :
Given that,
mean = = 7.7
standard deviation = = 0.19
n = 4
= = 7.7
= / n = 0.19 / 4 = 0.095
a) P(7.54< < 7.87)
= P[(7.54 - 7.7) / 0.095 < ( - ) / < (7.87 - 7.7) / 0.095 )]
= P( - 1.68< Z < 1.87)
= P(Z < 1.87) - P(Z < - 1.87)
Using z table,
= 0.9693 - 0.0307
= 0.9386
b) Using standard normal table,
P(Z < z) = 3 %
= P(Z < z ) = 0.3
= P(Z < z ) = 0.3
z = 0.5244
Using z-score formula
= z * +
= 0.5244 * 0.095 +7.7
= 7.75
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