Question

Answer the questions using the result of minitab. a) Binomial (n=92, p=0.38) Make a bar chart. Calculate P(X=56), P(X<59), P(X>49), P(49<X<59)? b) Normal (u=52, sd=18) Make a scatterplot. Calculate P(X=56), P(X<59), P(X>49), P(49<X<59), P(X<?) = .8? c) Simulation from binomial distribution (n=22, p=0.18) for 10000 rows, calculate relative frequency for all possible value of X d) Compare a normal distribution with u=40 and sd=8 to a normal distribution with u=45 and sd=5 by graph e) Calculate P(2<x<6) for Poisson(u=3)

Answer 1

Bar plot of binomial(92,0.38)

Probability Density Function

Binomial with n = 92 and p = 0.38

x P( X = x )
56 0.0000046

Cumulative Distribution Function

Binomial with n = 92 and p = 0.38

x P( X ≤ x )
59 1.00000

p(X<59)=P(X<=59)-P(X=59) =1-0.0000002
=0.9999998

Cumulative Distribution Function

Binomial with n = 92 and p = 0.38

x P( X ≤ x )
49 0.998946
hence P(X>x)=1-P(X<x)=1- 0.998946=0.001054

P(49<X<59)=P(X<59)-P(X<49)=0.9999998-0.998946 =0.0010538

QUE2

Probability Density Function

Normal with mean = 52 and standard deviation = 18

x f( x )
56 0.0216229 # is value of pdf at X=56

P(X=56)=0 since normal distribution is contineous

Normal with mean = 52 and standard deviation = 18

x P( X ≤ x )
59 0.651321

P(49<X<59)=0.651321- 0.433816 =0.217505

Inverse Cumulative Distribution Function

Normal with mean = 52 and standard deviation = 18

P( X ≤ x ) x
0.8 67.1492

Cumulative Distribution Function

Poisson with mean = 3

x P( X ≤ x )
6 0.966491

MTB > CDF 2;
SUBC> Poisson 3.

Cumulative Distribution Function

Poisson with mean = 3

x P( X ≤ x )
2 0.423190

P(2<X<6)=P(X<=6)-P(X=6)-P(X<=2)=0.966491-0.0504094- 0.423190

P(2<X<6)= 0.4928916