Question

A student studying for a vocabulary test knows the meanings of 12 words from a list of 22 words. If the test contains 10 words from the study list, what is the probability that at least 8 of the words on the test are words that the student knows? (Round your answer to three decimal places.)

Answer 1

Solution-:

Given:

Let,X- be the number of words selected in sample

This situation is suitable for hypergeometric distribution

The p.m.f. of X is ,

We use Binomial Aprroximation

i.e.  

We find P[at least 8 of the words on the test are words that the student knows]

  

	n=10	p=0.55	q=0.45
x	nCx	p^x	q^(10-x)	P[X=x]
0	1	1	0.000	0.000
1	10	0.55	0.001	0.004
2	45	0.3025	0.002	0.023
3	120	0.166375	0.004	0.075
4	210	0.091506	0.008	0.160
5	252	0.050328	0.018	0.234
6	210	0.027681	0.041	0.238
7	120	0.015224	0.091	0.166

From above table we write following probabilioties

Therefore , the reqired pbobability is equal to 0.100