In: Statistics and Probability
4 (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).
PLZ ANS THE 4a!
P[ She can work on weekdays ] = p = 75% = 0.75
Number of weekdays = n = 5 days
Find the expected value and the standard deviation of the number of days she exercises in a given week.
In these cases where the probability and n is given the formula used for mean is the mean of binomial
Mean = np = 5*0.75 = 3.75 days ( approx 4 ays )
In these cases where the probability and n is given the formula used for variance is the variance of binomial
variance = np(1-p) = 5*0.75(1-0.25) = 5*0.75*0.25 = 0.9375
To obtain the standard deviation, take square root of variance
standard deviation = sqrt(0.9375) = 0.9682