use the binomial distribution

Suppose that

25​%

of all home buyers will do some remodeling to their home within the first five years of home ownership. Assuming this is​ true, use the binomial distribution to determine the probability that in a random sample of

15

​homeowners,

4

or fewer will remodel their homes. Use the binomial table. 

he probability that

4

or fewer people in the sample indicate that they will remodel their homes is

nothing.
​(Round to four decimal places as​ needed.)                                    
 
n=15                
x p=0.10 p=0.15 p=0.2 p=0.25 p=0.30 p=0.35 p=0.40 p=0.45
0 0.205891132 0.087354219 0.035184372 0.013363461 0.004747562 0.001562069 0.000470185 0.000127479
1 0.549043019 0.318585976 0.167125767 0.080180766 0.0352676 0.014178785 0.005172035 0.001692001
2 0.815938931 0.604225204 0.398023209 0.236087811 0.126827715 0.061734095 0.027114001 0.01065244
3 0.94444437 0.822655202 0.648162105 0.461286876 0.296867928 0.172696487 0.090501902 0.042421269
4 0.987279516 0.938294613 0.835766276 0.686485942 0.515491059 0.351943428 0.217277706 0.120399305
5 0.99775033 0.983189914 0.93894857 0.851631923 0.72162144 0.564282111 0.40321555 0.260759769
6 0.999689369 0.996394414 0.981941193 0.94337969 0.868857427 0.754842468 0.609813156 0.452160402
7 0.999966375 0.999390393 0.99576025 0.982700162 0.94998746 0.886768869 0.786896817 0.653503925
8 0.999997154 0.999919095 0.999215015 0.995806986 0.984757474 0.957806162 0.904952592 0.818239535
9 0.999999813 0.999991662 0.999886774 0.999205051 0.996347479 0.987556823 0.966166697 0.923071287
10 0.999999991 0.999999346 0.999987538 0.999884664 0.999327766 0.997168575 0.990652339 0.974534147
11 1 0.999999962 0.999998989 0.999987636 0.999908341 0.999521102 0.998072231 0.993673227
12 1 0.999999998 0.999999943 0.999999077 0.999991281 0.99994335 0.999721096 0.998892976
13 1 1 0.999999998 0.999999957 0.999999483 0.999995819 0.999974767 0.999878523
14 1 1 1 0.999999999 0.999999986 0.999999855 0.999998926 0.999993717
15 1 1 1 1 1 1 1 1
n=20                
x p=0.10 p=0.15 p=0.2 p=0.25 p=0.30 p=0.35 p=0.40 p=0.45
0 0.121576655 0.038759531 0.011529215 0.003171212 0.000797923 0.000181245 3.65616E-05 6.41584E-06
1 0.391746998 0.175557876 0.06917529 0.024312625 0.00763726 0.00213312 0.000524049 0.000111402
2 0.676926805 0.404896278 0.206084719 0.091260432 0.035483132 0.012117707 0.003611472 0.000927434
3 0.867046677 0.647725174 0.411448862 0.225156048 0.107086805 0.044375603 0.015961163 0.004933408
4 0.956825505 0.829846846 0.629648264 0.414841503 0.237507779 0.118196559 0.050951953 0.018863272
5 0.988746866 0.932692026 0.804207785 0.617172654 0.416370829 0.245395745 0.125598973 0.055334188
6 0.997613911 0.978064899 0.913307486 0.785781948 0.608009812 0.416625418 0.250010672 0.129933789
7 0.999584365 0.994078854 0.967857337 0.898188143 0.772271797 0.601026605 0.415892938 0.252005863
8 0.999940141 0.998671092 0.990018214 0.959074832 0.886668537 0.762377643 0.595598725 0.414306234
9 0.999992849 0.999751618 0.997405173 0.986135583 0.952038103 0.878219414 0.755337203 0.591361185
10 0.999999291 0.999961367 0.999436586 0.996057858 0.982855184 0.946833386 0.872478754 0.75071064
11 0.999999942 0.999995017 0.999898271 0.999064608 0.994861838 0.980420645 0.943473633 0.869235029
12 0.999999996 0.99999947 0.999984837 0.999816296 0.99872112 0.99398473 0.978971073 0.941965903
13 1 0.999999954 0.999998155 0.999970488 0.999738953 0.998479338 0.993534125 0.978585644
14 1 0.999999997 0.99999982 0.999996187 0.99995706 0.999689425 0.998388475 0.993566448
15 1 1 0.999999986 0.999999613 0.99999445 0.999950059 0.999682969 0.998469256
16 1 1 0.999999999 0.99999997 0.999999457 0.999993916 0.999952655 0.999722815
17 1 1 1 0.999999998 0.999999962 0.999999472 0.999994959 0.999964142
18 1 1 1 1 0.999999998 0.999999971 0.999999659 0.99999705
19 1 1 1 1 1 0.999999999 0.999999989 0.999999884
20 1 1 1 1 1 1 1 1

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