please show work! thank you!! The amount of growth in a 15 day period for a popu
ID: 2918921 • Letter: P
Question
please show work! thank you!!The amount of growth in a 15 day period for a population ofsunflower plants was found to follow a normal distribution withmean 3.18 cm & standard deviation 0.53 cm. What percentage ofplants grow... (a) 4cm or more? (b) 3 cm or less? (c) between 2.5 & 3.5cm? (d) In what range do the middle 90% of all growth valueslie?
The amount of growth in a 15 day period for a population ofsunflower plants was found to follow a normal distribution withmean 3.18 cm & standard deviation 0.53 cm. What percentage ofplants grow... (a) 4cm or more? (b) 3 cm or less? (c) between 2.5 & 3.5cm? (d) In what range do the middle 90% of all growth valueslie?
Explanation / Answer
(a) 4cm or more?P(x>4)=ans. P(x=4)=0 since normal distribution is continuous
ans= P((x-3.18)/.53>(4-3.18)/.53)= P(z>1.55)
P(0<z<1.55)+P(z>1.55)=.5 or
ans= P(z>1.55)= .5-P(0<z<1.55)= .5-.4394=.0606
(b) 3 cm or less?
P(x<3)=ans= P(((x-3.18)/.53<(3-3.18)/.53)=P(z<-.34
P(z<-.34+P(-.34<z<0)=.5
P(z<-.34)=.5-P(-.34<z<0)= .5-P(0<z<.34)=.5-.1331=.3669
(c) between 2.5 & 3.5cm?
P(2.5<x<3.5)=ans=P((2.5-3.18)/.53< (x-3.18)/.53<(3.5-3.18)/.53)=P(-1.28<z<.60)
ans=P(-1.28<z<0+P(0<z<.6)=P(0<z<1.28)+.2257=.3997+.2257=.6254
(d) In what range do the middle 90% of all growth valueslie?
The middle lie in some interval with the mean as center. Call thisdistance from mean a.
P(3.18-a<x<3.18+a)=.9
2P(3.18<x<3.18+a)=.9
P((3.18-3.18)/.53<(x-3.18)/.53<(3.18+a-3.18)/.53)=P(0<z<a/.53)=.45
from the z table we see that a/.53=1.645 .. half way between.4495 and .4505
a= .53(1.645) or a= .87185
So the interval is 3.18-.8785 and 3.18+.8785 or 2.30815 and4.0585
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