Question

compute P(X) using the binomial probability formula. Then determine whether the normal distribution can be used to estimate the probability. If so, approximate P(X) using the normal distribution and compare the result with the exact probability.
n=50, p=0.7, and X=34 find P(X)

Answer 1

what are your thoughts?

Answer 2

Not sure how to solve this chapter has been confusing

Answer 3

you must have come across a formula for a binom distribution ... the binom thrm?

Answer 4

\[(p+q)^n=\binom{n}{0}p^0q^n+\binom{n}{1}p^1q^{n-1}+\binom{n}{2}p^2q^{n-2}+...+\binom{n}{n}p^nq^{n-n}\]
the kth term of the expansion defines P(x=k)
\[P(k)=\binom{n}{k}p^kq^{n-k}\]

Answer 5

if np and nq are both bigger than 5, a normal distribution can be used to approx a binomial ... with some adjustment

Answer 6

mean = np
sd = sqrt(npq)

and P(k) = the area between some 1/2 adjustments:
\[z_1=\frac{(k-.5)-np}{sd}\]
\[z_2=\frac{(k+.5)-np}{sd}\]
P(k) is just the area between z1 and z2