# Manatees

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Manatees are large sea creatures that live in the shallow water alone the coast of Florida. Many manatees are injured or killed each year by powerboats. Here are the data on manatees killed and powerboat registration (in thousands of boats) in Florida for the period 1984 to 1990.

Year Powerboats Manatees Killed γ χ2 γ2 χγ

Registration χ

1984 559 34 312481 1156 19006

1985 585 33 342225 1089 19305

1986 614 33 376996 1089 20262

1987 645 39 416025 1521 25155

1988 675 43 455625 1849 29025

1989 711 50 505521 2500 35550

1990 719 47 516961 2209 33793

SUMS 4508 279 2925834 11413 182096

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Manatees are large sea creatures that live in the shallow water alone the coast of Florida. Many manatees are injured or killed each year by powerboats. Here are the data on manatees killed and powerboat registration (in thousands of boats) in Florida for the period 1984 to 1990.

Year Powerboats Manatees Killed γ χ2 γ2 χγ

Registration χ

1984 559 34 312481 1156 19006

1985 585 33 342225 1089 19305

1986 614 33 376996 1089 20262

1987 645 39 416025 1521 25155

1988 675 43 455625 1849 29025

1989 711 50 505521 2500 35550

1990 719 47 516961 2209 33793

SUMS 4508 279 2925834 11413 182096

See attachment for details and questions

###### Education

- BSc , Wuhan Univ. China
- MA, Shandong Univ.

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- "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
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