26 If 30% of the people in a cornmunity use the Library in one year, find the pr

Question

26 If 30% of the people in a cornmunity use the Library in one year, find the probability that in a random sample of 15 people (a) At most 7 use the Library (b) Exactly 7 use the Library, (c) At least 5 use the Library, (d) No more than 2 use the Library (e) Not less than 10 use the Library. 27. A basketball player makes 70% of the free throws he shoots, what is the probability that he will make more than 7 throws (a) If he tries 15 free throws? (b) If he tries 10 free throws? 28. Approximately 5% of the eggs in a store are cracked. Suppose you buy a dozen eggs from the store. (a) What is the probability that no more than one of your eggs is cracked? Page 5

Explanation / Answer

Solution:-
26) Given that p = 0.30 , n = 15 q = 1 - p = 0.7

a) P(X <= 7) = 0.9498
=> P(0) + P(1) + P(2) + P(3) + P(4) + P(5) + P(6) + P(7)
= 0.0047+0.0305+0.0916+0.1700+0.2186+0.2061+0.1472+0.0811
= 0.9498

b) P(X = 7) = 0.0811

c) P(X >= 5 ) = 0.4845
= P(5) + P(6) + P(7) + P(8) + P(9) + P(10) + P(11) + P(12) + P(13) + P(14) + P(15)
= 0.2061 + 0.1472 + 0.0811 + 0.0348 + 0.0116 + 0.0030 + 0.0006 + 0.0001

d) P(X <= 2) = 0.1268

e) PX >= 10) = 0.0037

27)

Solution:- Given that p = 0.7 ,

a) n = 15

P(X > 7) = 0.94999

b) n = 10

P(X > 7) = 0.38278

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