# statistics

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How do you solve this problem? physical therapy reported that it has been estimated that 80 percent of all lower back pain cases are caused by weak trunk muscles. if 15 patients with lower back pain are examined, what's the probability that

1. exactly 10 have pain caused by weak trunk muscles

2. more than 8 have pain caused by weak trunk muscles

3. fewer than 6 have pain caused by weak trunk muscles

• statistics -

1. Prob(pain caused by w.t.m.) = .8
prob(pain not caused by w.t.m.) = .2

so prob(exactly 10 caused by w.t.m.)
= C(15,10)(.8^10)(.2^5)
= .10318

2. lots of calculations here,
more than 8 means
exactly 9 + exactly 10 + exactly 11 + ...+ exactly 15

= C(15,9)(.8^9)(.2^6) + C(15,10)(.8^10)(.2^5) + ... + C(15,15)(.8^15)

2. done in a similar way, except you want
exactly 0 + exactly 1 + .. + exactly 5
= C(15,0)(.2)15 + C(15,1)(.8)(.2^14) + ..

happy calculating.

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