6) What is the probability that a randomly selected day from 2013 will have a Group Trades total within 105,000 of the mean? =3421439 =508638.08

a)A set of exam scores is normally distributed and has a mean of 72.6 and a standard deviation of 9.3. What is the probability that a randomly selected score will be between 76 and 84?

b)Using all 1991 birth records in the computerized national birth certificate registry compiled by the National Center for Health Statistics (NCHS), statisticians Traci Clemons and Marcello Pagano found that the birth weights of babies in the United States are not symmetric ("Are babies normal?" The American Statistician, Nov 1999, 53:4). However, they also found that when infants born outside of the "typical" 37-43 weeks and infants born to mothers with a history of diabetes are excluded, the birth weights of the remaining infants do follow a Normal model with mean = 3432 g and standard deviation = 482 g. The following questions refer to infants born from 37 to 43 weeks whose mothers did not have a history of diabetes. Compute the z-score of an infant who weighs 2122 g. (Round your answer to two decimal places.) Approximately what fraction of infants would you expect to have birth weights between 2970 g and 4510 g? (Express your answer as a decimal, not a percent, and round to 4 decimal places.) Approximately what fraction of infants would you expect to have birth weights below 2970 g? (Express your answer as a decimal, not a percent, and round to 4 decimal places.) A medical researcher wishes to study infants with low birth weights and seeks infants with birth weights among the lowest 18%. Below what weight must an infant's birth weight be in order for the infant be included in the study? (Round your answer to the nearest gram.) c)A manufacturer knows that their items have a normally distributed lifespan, with a mean of 2.1 years, and standard deviation of 0.5 years.The 5% of items with the shortest lifespan will last less than how many years?

d)Eleanor scores 680 on the mathematics part of the SAT. The distribution of SAT math scores in recent years has been Normal with mean 578 and standard deviation 115. Gerald takes the ACT Assessment mathematics test and scores 27. ACT math scores are Normally distributed with mean 18.2 and standard deviation 3.5. (a) What is Eleanor's standardized score (z-score)?

Answer = Round to 3 decimal places.

(b) What is Gerald's standardized score?

Round to 3 decimal places.

(c) Assuming that both tests measure the same kind of ability, who has the higher score?

• Gerald.
• Eleanor.
• They both did equally well.