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In a certain school 40% of the students have opted for first language Kannada. Assuming 20 teachers take a sample of 4 students each, how many teachers will report that 2 or 3 students opted for first language Kannada?

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Let x be the numbers students opted first language kannada is a Binomnal variate with the parameters.

n = 4; P = 40% = 0.4; q = 1 – p = 0.6 and N = 20.

The p. m. f. is P(x) = nCxPx qn-x = 1 – p = 0.6 and N = 20

P(x) = 4Cx(0.4) x (0.6)4 – x ; x = 0,1,2,3,4

Number of teachers will report 2 or more students opted for first language kannada

= P(x = 2) + P(x = 3) = 4C2(0.4)2 (0.6)4 – 2 + 4C3(0.4)3(0.6)4-3

= 0.3456 + 0.1536 = 0.4992 × 20 = 9.98.

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