I posted a question earlier in the mathematics area and I really need some help. My husband passed away a few weeks ago and I am having a hard time understanding how to work these problems. I am doing a pretest and this is the last question and I have been working on it for two days. Please help!
If np ≥ 5, and nq ≥ 5, estimate P(fewer than 8) with n =14 and p = 0.6 by using the normal distribution as an approximation to the binomial distribution; if np

Question

I posted a question earlier in the mathematics area and I really need some help. My husband passed away a few weeks ago and I am having a hard time understanding how to work these problems. I am doing a pretest and this is the last question and I have been working on it for two days. Please help!
 If np  ≥ 5, and nq ≥ 5, estimate P(fewer than 8) with n =14 and p = 0.6 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. Please any one that can help!!

anonymous · Answer

your husband passed away?

phi · Answer

in your problem, n= 14 is the number of trials, p = 0.6 is the probability of the trial being a success. I think q is (1-p) = 1-0.6 = 0.4 np means 14 * 0.6= 8.4 nq means 14*0.4 = 5.6 both are bigger than 5, so (by a "rule of thumb"), we can use a gaussian distribution. according to wikipedia https://en.wikipedia.org/wiki/Binomial_distribution#Normal_approximation with mean np = 8.4 and standard deviation n*p*q = 14*0.6*0.4 = 3.36

phi · Answer

Pr(fewer than 8) using a normal distribution with mean 8.4 , std 3.36 means the area under the curve below 8. change 8 to how many standard deviations below the mean 8.4. we do this by subtracting the mean: 8- 8.4 = -0.4 and then dividing by the standard deviation: -0.4/3.36 = - 0.119 find the area under the curve. we get http://www.wolframalpha.com/input/?i=Pr%28x%3C-0.119%29

anonymous · Answer

I made a mistake P(fewer than 6) Sorry.