The cost to produce a batch of granola bars is approximately Normally distributed with a mean of $7.19 and a standard deviation of $0.86. If a random sample of 12 batches of granola bars is selected, what is the probability that the mean cost will be more than $7.00?

The sample mean has mean $7.19 and standard error $0.86/√12 ≈ $0.248. For a sample mean of $7.00, the z-score is (7.00 − 7.19)/0.248 ≈ −0.77. Thus, the probability the mean cost is more than $7.00 is P(Z > −0.77) ≈ 0.7780, so the correct choice is 0.7780.

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