The average amount of money spent for lunch per person in the college cafeteria is \$7.42 and the standard deviation is \$2.58. Suppose that 8 randomly selected lunch patrons are observed. Assume the distribution of money spent is normal, and round all answers to 4 decimal places where possible.

A) For a single randomly selected lunch patron, find the probability that this patron's lunch cost is between \$8.4717 and \$9.0778. ____

B) For the group of 8 patrons, find the probability that the average lunch cost is between \$8.4717 and \$9.0778. ____

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.

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