Transcutaneous electrical nerve stimulation (TENS) is used by doctors and physic

Question

Transcutaneous electrical nerve stimulation (TENS) is used by doctors and physical therapists for pain reduction. Suppose that typically this treatment reduces pain at least 2 levels on the 11-point pain scale for 55% of the patients treated. Let X be the number patients with this kind of reduction out of sample of 5 patients.

1. a.Find the probability that exactly three patients have the pain reduction.

b. Find the probability that less than two patients have the pain reduction.

c. Find the probability that more than 1 patients have the pain reduction.

Explanation / Answer

n = 5

p = 0.55

q = 1 - p = 0.45

P(X) = nCx px qn-x

a) Probability that exactly three patients have the pain reduction = P(3)

= 5C3 x 0.553 x 0.452

= 0.3369

b) Probability that less than two patients have the pain reduction = P(0) + P(1)

= 0.455 + 5x0.55x0.454

= 0.0185 + 0.1128

= 0.1313

c) Probability that more than 1 patients have the pain reduction = 1 - P(less than or equal to one patient have the pain reduction)

= 1 - 0.1313

= 0.8687

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