Question

In Hawaii shark attacks are very rare. Furthermore, 55% of all shark attacks are serious, but not fatal. You are scheduled to give a talk at a local scuba club in Honolulu and want to include a brief statistical profile regarding the most recent seven shark attacks, all of which were nonfatal. Let r be the number of non fatal attacks out of a random sample of seven shark attacks.
(b) what is the probability all seven shark attacks are nonfatal (round to 3 decimal places)

(c) what is the probability that four or more of the shark attacks were nonfatal (round to 3 decimal places)

(d) what is the expected number of nonfatal shark attacks out of the seven

(e) what is the standard deviation of the r-probability distribuation ( round tho 3 decimal places)

Answer 1

Pr(Shark Attacks are serious but not fatal) = 0.55

here number of shark attacks = 7

r = number of nonfatal attacks out of a random sample of seven shark attacks.

(a) Here x is the number of shark attacks that ar not fatal.

Pr(x = 7) = BIN(x = 7 ; 7 ; 0.55) = (0.55)⁷ = 0.0152

(b) Pr(x >= 4 ; 7 ; 0.55) = 1 - Pr(x < 4 ; 7 ; 0.55) = 1 - BINOMDIST (x < = 3 ; 7 ; 0.55)

= 1 - 0.3917 = 0.6083

(c) Expected number of nonfatal shark attacks out of seven = 7 * 0.55 = 3.85

(e) Here standard deviation of r probability distribution = sqrt(7 * 0.55 * 0.45) = 1.3162