The Eurelian School System pays bonuses to its physical-education teachers according to their body types. Eighty percent of Eurelian physical-education teachers are mesomorphs, fifteen percent are endomorphs, and the remaining five percent are ectomorphs. Seventy percent of mesomorphic physical-education teachers have tenure, and get bonuses of $10000 (Eurelian dollars). Sixty percent of endomorphic physical-education teachers have tenure, and get bonuses of $7500 (Eurelian dollars). Thirty percent of ectomorphic physical-education teachers have tenure, and get bonuses of $2000 (Eurelian dollars). The non-tenured physical-education teachers all get bonuses of $1000 (Eurelian dollars).

a)Find the mean and standard deviation in the bonuses of Eurelian physical-education teachers.

b)Of those who get bonuses less than $6000 (Eurelian), what proportion have tenure?

c)Use a numerical criterion to determine whether the events 'having tenure' and 'endomorph' are statistically independent.

d)Show that the z-score of $1000 (Eurelian) is -1.35, to two decimal places of accuracy.