Question

In: Statistics and Probability

4 (a) Susan tries to exercise at ”Pure Fit” Gym each day of the week, except...

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).

  1. Find the expected value and the standard deviation of the number of days she exercises in a given week.    [2 marks]
  2. Given that Susan exercises on Monday, find the probability that she will exercise at least 3 days in the rest of the week. [3 marks]
  3. Find the probability that in a period of four weeks, Susan exercises 3 or less days in only two of the four weeks.      [3 marks]

PLZ ANS THE 4a!

Solutions

Expert Solution

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


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