The distribution of scores on the SAT is approximately normal with a mean of μ = 500 and a standard deviation of σ = 100. For the population of students who have taken the SAT, a. What proportion have SAT scores less than 350? b. What proportion have SAT scores greater than 720? c. What is the minimum SAT score needed to be in the highest 25% of the population? d. If the state college only accepts students from the top 44% of the SAT distribution, what is the minimum SAT score needed to be accepted?

Suppose you have already calculated the mean, the average deviation, and the standard deviation of the weights in pounds of 20 third-graders.  a. if these weights were converted to kilograms and the mean and the average deviation were once again calculated, would the second average deviation be (numerically) less than, greater than, or equal to the first average deviation? Explain your answer. b. If the standard deviation of these weights were calculated in kilograms, would it be (numerically) less than, greater than, or equal to the first standard deviation? Explain your answer

A data set lists weights (Ib) of plastic discarded by households. The highest weight is 5.72 Ib, the mean of all of the weights is x= 2.345 lb, and the standard deviation of the weights is s =2.123 lb. a. What is the difference between the weight of 5.72 lb and the mean of the weights? b. How many standard deviations is that (the difference found in part (a))? c. Convert the weight of 5.72 Ib to a z score d. If we consider weights that convert to z scores between -2 and 2 to be neither significantly low nor significantly high, is the weight of 5.72 Ib significant? a. The difference is lb. (Type an integer or a decimal. Do not round.) b. The difference is standard deviations. (Round to two decimal places as needed.) c. The z score is z= (Round to two decimal places as needed.) d. The highest weight is

The mean mathematics score for seniors who took the SAT in 2018 was 531. If the standard deviation for this same year was 118, what is the z score for a person who received an SAT mathematics score of 685? a. -1.31 b. -0.77 c. +1.31 d. +0.77

In a certain population, the mean score on a test is 420.  The standard deviation is 105. If the distribution or scores is normal, which of these scores should occur most often. a. 385 b314 c. 540  d. 526