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Mean weight of the given weights = μ = 67.8 kg
We assume that the mean weight of the population is 67.8 kg.

Standard deviation = σ = 8.16 kg

Normal distribution variable is Z.  Ztable (z) gives area under the normal distribution curve between Z=0 and z.  The area gives the probability.

Z = (X - μ ) / σ =   (66 - 67.9) / 8.16 kg = - 0.2328

ZTable(-0.2328) = Ztable (0.2328) = 0.091

The weight 66 kg is far from estimated mean of 67.9 kg by probability of 0.091 or 9.1 %.  The error margin should be at least 9.1% to say that 66kg can be considered to be the mean weight of the population.

0.091 is 9.1 % significance level.

So the claim that the mean weight in the population is 66 kg at 5% level of significance is WRONG.