The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.3 ounce. a) What is the probability that a randomly selected carton has a weight greater than 10.12 ounces? The average math SAT score is 522 with a standard deviation of 113. A particular high school claims that its students have unusually (b) A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 10.12 ounces? high math SAT scores. A random sample of 55 students from this school was selected, and the mean math SAT score was 544. Is the high school justified in its claim? Explain. (a) The probability is. (Round to four decimal places as needed.) , because the z-score () is since it within the range of a usual event, namely within (b) The probability is. of the mean of the sample means. Round to four decimal places as needed.) (Round to two decimal places as needed.) Determine whether the statement is true or false. If it is false, rewrite it as a true statement. The weights of ice cream cartons are normally distributed with a mean weight of 10 ounces and a standard deviation of 0.3 ounce. As the size of a sample increases, the standard deviation of the distribution of sample means increases. (a) What is the probability that a randomly selected carton has a weight greater than 10.12 ounces? (b) A sample of 36 cartons is randomly selected. What is the probability that their mean weight is greater than 10.12 ounces? Choose the correct choice below. (a) The probability is. A. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of (Round to four decimal places as needed.) sample means does not change." (b) The probability is. O B. This statement is false. A true statement is, "As the size of a sample decreases, the standard deviation of the distribution of sample means decreases." (Round to four decimal places as needed.) O C. This statement is true O D. This statement is false. A true statement is, "As the size of a sample increases, the standard deviation of the distribution of sample means decreases."