Question

STAT 353 Homework 3 STAT 353: Homework 3 (Probability Distributions) Points Possible: 10 Problems: . A synthetic fabric is produced in continuous rolls of uniform width. The probability distribution of the number of imperfections per 10 meters is given in the table. 0 # imperfections probability 4 0.41 0.37 0.16 0.05 0.01 a) b) What is the expected number of imperfections in a 10 meter section? Find the standard deviation in the number of imperfections per 10 meter section.

please do this probability problem and please explain
thank you

Answer 1

a) Expected value = Sum of {xP(x)}

= 0x0.41 + 1x0.37 + 2x0.16 + 3x0.05 + 4x0.01

= 0.88

b) variance = Sum of {(x-mean)² p(x)}

= (0 - 0.88)²x0.41 + (1 - 0.88)²x0.37 + (2 - 0.88)²x0.16 + (3 - 0.88)²x0.05 + (4 - 0.88)²x0.01

= 0.8456

standard deviation = $\sqrt{0.8456}$

= 0.9196