Answer to Question #168233 in Statistics and Probability for kyanna Hoshino

Question

The probabilities of a machine manufacturing 0, 1, 2, 3, 4, or 5defective parts in one day are 0.75, 0.17, 0.04, 0.025, 0.01, and 0.005, respectively. The computed variance is _____ and standard deviation is _____ of the distribution.

NOTE: Round off your answer to the nearest hundredths

Answer 1

The expected value $μ = 0 \times 0.75 + 1 \times 0.17 + 2 \times 0.04 + 3 \times 0.025 + 4 \times 0.01 + 5 \times 0.005$

$= 0 + 0.17 + 0.08 + 0.075 + 0.04 + 0.025 \\ = 0.39$

Variance:

$σ^2 = (0-0.39)^2 \times 0.75 + (1-0.39)^2 \times 0.17 + (2-0.39)^ \times 0.04 + (3-0.39)^2 \times 0.025 + (4-0.39)^2 \times 0.01 + (5-0.39)^2 \times 0.005 \\ = 0.114 + 0.063 + 0.103 + 0.170 + 0.130 + 0.106 \\ = 0.686$

The standard deviation:

$σ = \sqrt{σ^2} = \sqrt{0.686} = 0.828$

The computed variance is 0.686 and standard deviation is 0.828 of the distribution.