Estimate the indicated probability by using normal distribution as an approximation to the binomial distribution. Estimate P(6) for n=18 p=0.3

Answer:P(6) = 0.6217Step-by-step explanation: To find P(6), which is the probability of getting a 6 or less, we will need to first calculate two things: the mean of the sample (also known as the "expected value") and the standard deviation of the sample.   Mean = np Here, "n" is the sample size and "p" is the probability of the outcome of interest, which could be getting a heads when a tossing a coin, for instanc So, Mean = n × p = (18) ×(0.30) = 5.4 Next we we will find the standard deviation: Standard Deviation = [tex]\sqrt{npq}[/tex] n = 18  and  p = 0.3   "q" is simply the probability of the other possible outcome (maybe getting a tails when flipping a coin), so   q = 1 - p Standard Deviation =[tex]\sqrt{npq} = \sqrt{(18)(0.3)(0.7)}[/tex]                                                               = 1.944 Now calculate the Z score for 6 successes.   Z = ( of successes we're interested in - Mean) ÷ (Standard Deviation) =(6-5.4)  ÷ (1.944) = 0.309 we have our Z-score, we look on the normal distribution and find the area of the curve to the left of a Z value of 0.309.  This is basically adding up all of the possibilities for getting less than or equal to 6 successes.  So, we get 0.6217.