Question

A certain variety of flower seed is sold in packets containing 1000 seeds. It is claimed on the packet that 40% will bloom white and 60% will not bloom red. This may be assumed accurate. 200 seeds are planted for experimental purposes.

Find the probability that half of our experimental plants will bloom white.

Find the probability that between 60 and 90 inclusively will bloom white

Find the probability that exactly 125 will bloom red.

Find the probability that more than the percentage that bloomed white will bloom red in the 200 experimental seed plantation

Answer 1

a)

X = 100

P ( X = 100) = C (200,100) * 0.4^100 * ( 1 - 0.4)^100=

=0.0010

b)

P ( X = 60) = C (200,60) * 0.4^60 * ( 1 - 0.4)^140=	60	0.0008
P ( X = 61) = C (200,61) * 0.4^61 * ( 1 - 0.4)^139=	61	0.0013
P ( X = 62) = C (200,62) * 0.4^62 * ( 1 - 0.4)^138=	62	0.0019
P ( X = 63) = C (200,63) * 0.4^63 * ( 1 - 0.4)^137=	63	0.0027
P ( X = 64) = C (200,64) * 0.4^64 * ( 1 - 0.4)^136=	64	0.0039
P ( X = 65) = C (200,65) * 0.4^65 * ( 1 - 0.4)^135=	65	0.0054
P ( X = 66) = C (200,66) * 0.4^66 * ( 1 - 0.4)^134=	66	0.0074
P ( X = 67) = C (200,67) * 0.4^67 * ( 1 - 0.4)^133=	67	0.0099
P ( X = 68) = C (200,68) * 0.4^68 * ( 1 - 0.4)^132=	68	0.0129
P ( X = 69) = C (200,69) * 0.4^69 * ( 1 - 0.4)^131=	69	0.0164
P ( X = 70) = C (200,70) * 0.4^70 * ( 1 - 0.4)^130=	70	0.0205
P ( X = 71) = C (200,71) * 0.4^71 * ( 1 - 0.4)^129=	71	0.0250
P ( X = 72) = C (200,72) * 0.4^72 * ( 1 - 0.4)^128=	72	0.0299
P ( X = 73) = C (200,73) * 0.4^73 * ( 1 - 0.4)^127=	73	0.0349
P ( X = 74) = C (200,74) * 0.4^74 * ( 1 - 0.4)^126=	74	0.0400
P ( X = 75) = C (200,75) * 0.4^75 * ( 1 - 0.4)^125=	75	0.0448
P ( X = 76) = C (200,76) * 0.4^76 * ( 1 - 0.4)^124=	76	0.0491
P ( X = 77) = C (200,77) * 0.4^77 * ( 1 - 0.4)^123=	77	0.0527
P ( X = 78) = C (200,78) * 0.4^78 * ( 1 - 0.4)^122=	78	0.0554
P ( X = 79) = C (200,79) * 0.4^79 * ( 1 - 0.4)^121=	79	0.0570
P ( X = 80) = C (200,80) * 0.4^80 * ( 1 - 0.4)^120=	80	0.0575
P ( X = 81) = C (200,81) * 0.4^81 * ( 1 - 0.4)^119=	81	0.0568
P ( X = 82) = C (200,82) * 0.4^82 * ( 1 - 0.4)^118=	82	0.0549
P ( X = 83) = C (200,83) * 0.4^83 * ( 1 - 0.4)^117=	83	0.0521
P ( X = 84) = C (200,84) * 0.4^84 * ( 1 - 0.4)^116=	84	0.0484
P ( X = 85) = C (200,85) * 0.4^85 * ( 1 - 0.4)^115=	85	0.0440
P ( X = 86) = C (200,86) * 0.4^86 * ( 1 - 0.4)^114=	86	0.0392
P ( X = 87) = C (200,87) * 0.4^87 * ( 1 - 0.4)^113=	87	0.0343
P ( X = 88) = C (200,88) * 0.4^88 * ( 1 - 0.4)^112=	88	0.0293
P ( X = 89) = C (200,89) * 0.4^89 * ( 1 - 0.4)^111=	89	0.0246
P ( X = 90) = C (200,90) * 0.4^90 * ( 1 - 0.4)^110=	90	0.0202

= 0.9332

c)

P ( X = 125) = C (200,125) * 0.6^125 * ( 1 - 0.6)^75=

=0.0448

d)

	X	P(X)			P(>X)
P ( X = 100) = C (200,100) * 0.6^100 * ( 1 - 0.6)^100=	100	0.0010			0.9974

= 0.9974

THANKS

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