Math 150 Stats.

Question

n=7, p =0.67

to find the following Binomial probability

P(4) = 

Answer 1

mean = np = 7(.67) = 4.69

variance = npq = 4.69(.31) = 1.4539

standard deviation

square root of variance

= sqr(1.4539)

= 1.057778

= about 1.206

z = 4.69-4)/1.206= about .5721

P(0<x<z)= amost 22%

is an approximation

closer is the following:

P(4 out of 7) = 7C4(p^4)q^3)

= 7!/4!3!(.67)^4(.31)^3

=35(.2015)(.0298)

=about .21

=about 21%