Although I already asked this , when I answered, it wasn't what the teacher wanted
A. Find the binomial probability P(x=5) where n=13 and p=0.50
B. Set up , without solving, the binomial probability P (x is at most 5), using probability notation
C. How would you find the normal approximation to the binomial probability P(x=5) in Part A. How would you calculate the mean and standard deviation in the formula for the normal approximation to the binomial and give the final formula without going through calculations. Thank you
A. Find the binomial probability P(x=5) where n=13 and p=0.50
B. Set up , without solving, the binomial probability P (x is at most 5), using probability notation
C. How would you find the normal approximation to the binomial probability P(x=5) in Part A. How would you calculate the mean and standard deviation in the formula for the normal approximation to the binomial and give the final formula without going through calculations. Thank you
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qA
P[x = 5] = 13c5 *(1/2)^5 *(1/2)^8 = 13c5/2^13 = 0.1571
[ note that the formula simplifies to P[x]= nCx /2^n when p=1/2 ]
qB
P[x ≤5] = (5c0 + 5c1 + 5c2 + 5c3 + 5c4 + 5c5)/2^13 <------
qC
a. µ = np
b. σ = √(npq)
c. with continuity correction, x = 5 becomes 4.5 ≤ x ≤ 5.5
d. z1 = (4.5-µ)/σ , z2 = (5.5-µ)/σ
e. P(x = 5) = P(z1 ≤ z ≤ z2)
P[x = 5] = 13c5 *(1/2)^5 *(1/2)^8 = 13c5/2^13 = 0.1571
[ note that the formula simplifies to P[x]= nCx /2^n when p=1/2 ]
qB
P[x ≤5] = (5c0 + 5c1 + 5c2 + 5c3 + 5c4 + 5c5)/2^13 <------
qC
a. µ = np
b. σ = √(npq)
c. with continuity correction, x = 5 becomes 4.5 ≤ x ≤ 5.5
d. z1 = (4.5-µ)/σ , z2 = (5.5-µ)/σ
e. P(x = 5) = P(z1 ≤ z ≤ z2)