In a certain school 40% of the students have opted for first language

1.	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?
Answer» 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) = ⁿC_xP^x q^n-x = 1 – p = 0.6 and N = 20 P(x) =⁴C_x(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.

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?

Answer»

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) = ⁿC_xP^x q^n-x = 1 – p = 0.6 and N = 20

P(x) =⁴C_x(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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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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