Please help with the following questions:

1. Suppose you had a population of fish whose lengths were normally distributed with a mean of 50 centimeters and a standard deviation of 5 centimeters. You draw a simple random sample of size 10, record the length of each fish, and calculate the mean of the sample lengths. What do you think your sample mean would most likely be? Explain your answer using what you know about random samples and sample means.

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You're a contestant in a game show called Estimate This! The object of the game is to estimate a value, which you state as a number plus or minus 1%, 2%, 3%, 5%, 10%, or 15%. For instance, if you're asked to guess the point spread in the next Superbowl, you can say "I guess 7 points, plus or minus 5%." Here's what makes the game interesting: For correct guesses, the narrower your interval (the range of your plus or minus values), the more you win. +% Winnings #152% $100.00 #10% $500.00 +5% $5,000.00 $3% $10,000.00 +2% $20,000.00 #1% $40,000.00 If you guess wrong (that is, if the number isn't within the interval you guessed), you win nothing. Here's a summary of the rules: 1. You guess a number, plus or minus a percentage. 2. If the number you're trying to guess is within the interval, you win. The narrower your interval, the more money you win. 3. If the number isn't within the interval, you don't win anything. Make a guess, stated as a number plus or minus 1%, 2%, 3%, 5%, 10%, or 15%, for one or more of the questions listed below. Explain the reasoning behind your guess and indicate how confident you are it's correct. Question In the next league game played at your school (it can be any sport as long as you specify which it is), what will the point spread be at the end of the game? Give a reason for your guess, and state how confident you are that you're correct