Reference no: EM132848143

1. In a certain population of fish, lengths are approximately normally distributed with a mean of 58mm and standard deviation of 3mm.

a) According to the Empirical Rule, approximately 99.7% of the fish will have lengths between what two values?

b) Find the Z-score for a fish that is 52mm long, then provide a one-sentence interpretation of what the Z-score tells you about that how that fish compares to the rest of the population.

c) What is the 75th percentile for length in this population?

d) What proportion of fish are longer than 60mm?

e) What is the probability that a randomly selected fish is shorter than 56mm?

2. According to the Empirical Rule, approximately 95% of observations are between ± 2 in the middle of the standard normal (Z) distribution. Recall that the Z distribution has a mean of 0 and standard deviation of 1. To three decimal places, what two values would enclose exactly 95% in the middle? Hint: use InvNorm and consider if the 95% is exactly in the middle, how much would be in each tail?