Statistical Question

Question

If np≥5 and nq≥ 5 estimate P(more than 4) with n=14 and p = 0.7 by using the normal distribution as an approximation to the binomial distribution if np<5 or nq<5, then state tha the normal approximation is not suitable.

 

Choices:

A) P(more than 4) = ____ ( four decimal places)

B) The normal distribution cannot be used

Answer 1

np>/=5, n(1-p)>/=5, n - np>/=5

add 1st and last to get

n >/=10, n=14, p=.7, q=.3, npq = 14(.7)(.3) = 14(.21) = 147/50 = 294/100 = 2.94

standard deviation = sqrnpq = sqr2.94 = .7sqr6= about 1.715

and np = x bar = mean = 9.8

Pr(x>4) has z score = (4-9.8)/1.7 = -5.8/1.7= about -3.38

use a z calculator or z tables to find the probability or

by the empirical rule Pr(x>4) = more than .5+99.7/2 = .5+49.85 = .99.85 = nearly 100 percent

but then np is not less than 5, although nq is. np=14(.7) = 9.8, nq = 14(.3) = 4.2