Question

6) In a high risk group, the chances of a person having suffered a heart attack are 53.24%. If nine people are chosen, find the following probabilities: a) P(X-3) b) P(X> 7) c) P(X < 6) d) P(at least 5) e) P(no more than 2)

(please, show work)

Answer 1

Q.6) Let X be Binomial random variable with n = 9 and p = 0.5324

Using Excel we find, the following probabilities,

a) P(X = 3) = BINOMDIST(3, 9, 0.5324, 0) = 0.13250749

=> P(X = 3) = 0.13250749

b) P(X > 7)

= 1 - P(X <= 7)

= 1 - BINOMDIST(7, 9, 0.5324, 1)

= 0.03060244

=> P(X > 7) = 0.03060244

c) P(X < 6)

= P(X <= 5)

= BINOMDIST(5, 9, 0.5324,1)

= 0.67837734

=> P(X < 6) = 0.67837734

d) P(at least 5)

= P(X >= 5)

= 1 - P(X < 5)

= 1 - P(X <= 4)

= 1 - BINOMDIST(4, 9, 0.5324, 1)

= 0.57928965

=> P(at least 5) = 0.57928965

e) P(no more than 2)

= P(X <= 2)

= BINOMDIST(2, 9, 0.5324, 1)

= 0.06189729

=> P(no more than 2) = 0.06189729