Question

Consider a surgical procedure to rebuild damaged cartilage in the knee. According to previous surgeries, the procedure has an 85% of succeeding with no further complications. A doctor performs this procedure 20 times.
(a) The doctor would like to use the normal approximation for binomial. Find the mean and standard deviation for ¯ x calculated from the sample.

(b) The doctor is interested in calculating the probability of seeing at most one person with a future complication. State this using probability notation and denote what X signifies. (c) Calculate this probability using the standard deviation above. (d) After performing the above calculations, is the normal approximation for binomial appropriate here? (e) Calculate the probability of the above calculation using the binomial distribution.

Answer 1

(a) Mean = 20*0.85 = 17

The Standard deviation = 20*0.85*0.15 = 1.597

(b) X ~ N(17, 1.597)

(c) 17 + 1*1.597 = 18.597

(d) Yes, n*p = 20*0.85 5

n*q = 20*0.15   5

(e) z = (18.597 - 17)/1.597 = 1

The probability is 0.8413.

Please give me a thumbs-up if this helps you out. Thank you!