The evolution of blind cave forms of the fish Astyanax mexicanus is associated with large reductions in the amount of time spent sleeping. The eyed, surface forms sleep about 800 minutes per 24-hour day (about 13 hours). The accompanying graph shows the frequency distribution of sleep times per 24 hours for 23 blind individuals from a single cave population (Duboué et al. 2011). The sample mean is 129.4 and the standard deviation is 147.2. Assume that the sample is a random sample.

a. Using the formula in Section 11.7, calculate a 95% confidence interval for mean sleep time in the cave population.

b. Use the graph to evaluate whether the assumptions of the confidence interval are likely to be met. Explain your answer.

c. In light of your answer in part (b), can we trust the confidence interval you calculated in part (a)?

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Frequency 10 8 1.0 A 2- 01 0 100 200 300 Time sleeping (min) 400 500