DO NOT LIKE MATH!!!!

Question

COULD SOMEONE GIVE ME THE ANSWER PLEASE I CAN'T THINK ANYMORE!!!!

 

If np ≥ 5 and nq ≥ 5, estimate P(fewer than 7) with ne=14 and p = 0.5 by using the normal distribution as an approximation to the binomial distribution; if np < 5 or nq < 5, then state that the normal approximation is not suitable. Which would be the correct response.

A. P (fewer than 7) = ?

B. The normal approximation is not suitable  

Answer 1

np >/= 5

nq >/=5

p=.5 = 1/2

q = 1-p=1-.5=.5

np = .5n

nq =.5n

5n >/= 5

n >/= 1

n=14

Var = npq = 14(.5)(.5)= 14/4 = 7/2

Standard Deviation =sqrVar = sqr(7/2) = (sqr14)/2

P(<7) = 50% = 1/2 = .5

mean =np = 14(1/2) = 7

half the distribution is below the mean, half above

but the binomial distribution is only an approximation to the normal distribution

and all distributions tend to be only approximations to the normal

an approximation of an approximation tends to lose some accuracy

but the binomial does seem to get the mean more correctly, more so than getting the standard deviation correct. Still the distribution may be skewed, so half the distribution may not be below the mean