Question

(a) Susan tries to exercise at ”Pure Fit” Gym each day of the week, except on the weekends (Saturdays and Sundays). Susan is able to exercise, on average, on 75% of the weekdays (Monday to Friday). Find the probability that in a period of four weeks, Susan exercises 3 or less days in only two of the four weeks.

Answer 1

for 1 week:

here this is binomial with parameter n=5 and p=0.75

Susan exercises 3 or less day in a week:

P(X<=3)=

∑x=03     (5Cx)px(1−p)(n-x)    =

0.3672

for 4 weeks:

this is binomial with parameter n=4 and p=0.3672

probability that in a period of four weeks, Susan exercises 3 or less days in only two of the four weeks:

P(Y=2) =(4C2)*(0.3672)²*(1-0.3672)² =0.3240