Z₁=(8.4717-7.42)/2.58=0.4076, Z₂=(9.0778-7.42)/2.58=0.6426.
(A) p(Z₁)=0.6582, p(Z₂)=0.7397, so the probability for the defined range is the difference between these probabilities: 0.0815 approx. This applies to one individual.
(B) In the sample group of 8, the number of degrees of freedom is 7. The SD needs to be adjusted for the sample: 2.58/√8=0.9122 and we use the t test.
t₁=(8.4717-7.42)/0.9122=1.1530, t₂=(9.0778-7.42)/0.9122=1.8174.
From t tables with dof=7, p(t₁)=0.1443, p(t₂)=0.0419, and the difference is 0.1024 approx. This is slightly higher than the probability for one individual.
