SOLUTION: This problem is really difficult. Please show me how to solve it: 14. On average, a telemarketer makes one sale in every six calls. If she makes 180 calls, find the probability

Question 442455: This problem is really difficult. Please show me how to solve it:
14. On average, a telemarketer makes one sale in every six calls. If she makes 180 calls, find the probability that she will make at least 38 sales. (Use normal approximation, 4 digits after decimal point.)
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Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
On average, a telemarketer makes one sale in every six calls. If she makes 180 calls, find the probability that she will make at least 38 sales. (Use normal approximation, 4 digits after decimal point.)
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Binomial Problem
with n = 180 and p = 1/6
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P(38<= x <=180) = ?
mean = np = 180*(1/6) = 30
std = sqrt(npq) = sqrt(30*(5/6)) = 5
Using normal approximation, find P(37.5 <= x <=180.5)
z(37.5) = (37.5-30)/[5] = 1.5
z(180.5) = (180.5-30)/(5) = 10.1
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So, P(38<= x <=180) = P(1.5<= z<=10.1) = 0.0668
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Cheers,
Stan H.
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