Central Limit Theorem - Mixed Problems CLT for Means x = mean CLT for Sums x= meann and s= SDVn 2-Score z = x-mean/s Directions: State if the problem is CLT for Means or CLT for Sums Identify all information and sketch a graph for the probability problems. 5. An unknown distribution is created by the birthweight of baby gorillas at a specific zoo. This distribution has a mean of 3.5 pounds and a standard deviation of .75 pounds. A sample, with size n = 25, was randomly drawn from all gorillas born at the zoo. What is the probability that the sample mean is between 4 and 5 pounds? 6. An unknown distribution is created by the average number of grams of silver per million gallons of seawater. This distribution has a mean of .45 grams and a sample standard deviation of .25 grams. A sample, with size 101 gallons, was randomly drawn from the population. What is the probability that the sample mean is greater than 1 gram? 7. The speeds of vehicles traveling on a highway have an unknown distribution with mean 71 and standard deviation 4 miles per hour. A sample, with size n = 37, is randomly drawn from the population and the sum is taken. What is the probability that the sum is between 2606 and 2612 miles per hour? 8. Assume that the weights of giant pumpkins have an unknown distribution with a mean of 35 pounds and a standard deviation of 5 pounds. A sample of size n = 45 is randomly taken from the population. What is the probability that the sample mean is in between 36 pounds and 37 pounds? Round your answer to three decimal places