Answer to Question #111170 in Statistics and Probability for loli

Question

[img]https://upload.cc/i1/2020/04/21/CjaDN6.jpg[/img]



B=4

Answer 1

(a) z=(x-mean)/sd= (15-11.5)/2.2=1.59

P(X<15)=0.944 ( using table Ф(1.59))

(b) P(X>k)=0.84

Ф(z)=1-0.84=0.16

using table z= -0.99

z=(k-mean)/sd

k=z*sd+mean=2.2*(-0.99)+11.5=9.32

(c) The central limit theorem states that the sampling distribution of the mean of any independent, random variable will be normal or nearly normal, if the sample size is large enough

mean of the sampling distribution:

Ms=mean=11.5

standart deviation of the sampling distribution:

S=sd/sqrt(N)=2.2/sqrt(36)=0.36

z=(x-Ms)/S=(11-11.5)/0.36=-1.38

P(x<11)=0.838