Based on Table 5.14 on page 213, what is the probability that x=5 for a Binomial

Question

Based on Table 5.14 on page 213, what is the probability that x=5 for a Binomial distribution with n=10 and p=0.3?

0.1029

0.0368

0.1536

A.

0.1029

B.

0.0368

C.

0.1536

probability of earning a score A that we need to answer this question. The of 70% or better is the sum of the four probabilities under the TABLE 5.14 I BINOMIAL PROBABILITY TABLES FROM APPENDIx A n x 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 10 0 0.3487 0.1969 0.1074 0.0563 0.0282 0.0135 0.0060 0.0025 0.0010 1 0.3874 0.3474 0.2684 0.1877 0.1211 0.0725 0.0403 0.0207 0.0098 2 o 1937 0.2759 0.3020 0.2816 0.2335 0.1757 0.1209 0.0763 0.0439 3 0.0574 0.1298 0.2013 0.2503 0.2668 0.2522 0.2150 0.1665 0.1172 4 0.01 12 0.0401 0.0881 0.1460 0.2001 0.2377 0.2508 0.2384 0.2051 5 0.0015 0.0085 4 0.0584 0.1029 0.1536 0.2007 0.2340 0.2461 6 0.0001 0.0012 55 0.0162 0.0368 0.0689 0.1115 0.1596 0.205 1 7 0.0000 0.0001 0.0008 0.0031 0.0090 0.0212 0.0425 0.0746 0.1172 8 0.0000 0.0000 0.0001 0.0004 0.0014 0.0043 0.0106 0.0229 0.0439 9 0.0000 0.0000 0.0000 0.0000 0.0001 0.0005 0.0016 0.0042 0.0008 10 0.0000 0.0000 0.0000 0.0000 0.0000 00 0.0001 0.0003 0.0010

Explanation / Answer

Binomial Distribution
PMF of B.D is = f ( k ) = ( n k ) p^k * ( 1- p) ^ n-k
Where   
k = number of successes in trials
n = is the number of independent trials
p = probability of success on each trial
P( X = 5 ) = ( 10 5 ) * ( 0.3^5) * ( 1 - 0.3 )^5
= 0.1029

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