Question

(a) The probability of a defective item produced by a machine is 0.20.

Find the probability that at least 3 of the 5 next items produced by

a machine will be in this defective.

(b) Analyze skewness of the following data with formula and diagram.

1,2,5,2,3,1,3,1.

Answer 1

a] the probability of a defective item is ,

the probability that at least 3 of the 5 next items produced is defective is given by

number of bernoulli trials ,

failure probability ,

the probability is given by

we get

b] we have the data as

1	-1.25	1.5625	-1.953125
2	-0.25	0.0625	-0.015625
5	2.75	7.5625	20.796875
2	-0.25	0.0625	-0.015625
3	0.75	0.5625	0.421875
1	-1.25	1.5625	-1.953125
3	0.75	0.5625	0.421875
1	-1.25	1.5625	-1.953125

we get mean as

the skewness is given by

since the value is between 0.5 and 1 , we get the distribution as moderately skewed