Question

2) In the year 2030, Sophie Hoare is using her background in mathematics to do player analysis in her role as coach of New Zealand’s women’s soccer team. Sophie is presently researching the number of years of training for women to be competitive at the professional level. Suppose this time is normally distributed with a mean of 12 years and a standard deviation of 2.1 years.

a) In a random sample of 9 professional soccer players, what is the probability the sample mean is more than 14 years? Would you classify this observation as an outlier? Why or why not?

b) What is the probability a randomly selected soccer player had more than 14 years of training? Would you classify this observation as an outlier? Why or why not?

c) What is the Interquartile Range (IQR) for the number of years of training?

d) If you took a random sample from this population and constructed a box-and-whisker plot, approximately what would be the three values on the box?

e) One professional soccer player’s length of training was 1.54 standard deviations above the mean. How many years of training did this player have?

f) Using Z > 2 as a criterion for an outlier, what is the minimum sample size such that a sample mean of 12.5 years would be classified as an outlier?

g) Sophie is developing new techniques with the goal of decreasing the number of years of training required to be competitive at the professional level.    Sophie desires the population mean to be such that in a random sample of 9 professional soccer players the probability the sample mean is less than 11 years is 0.8 (assume the population standard deviation = 2.1 years). In order to accomplish Sophie’s goals, the population mean can be no more than ___?

Answer 1

answered by: anonymous