Question

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 1

Answer:

P(6) = 0.6217

Step-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 = $\sqrt{npq}$

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 =$\sqrt{npq} = \sqrt{(18)(0.3)(0.7)}$  

                                                            = 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.