Question

A binomial experiment consists of 500 trials with the probability of success for each tria 3 What is the probability of obtaining 173 or more successes? (This binomial experimentally passes the nude of thumb lest as you can check. When computing the probability, adjust the given interval by extending the range by 05 on each side) IT Click the icon to view the area under the standard normal curve table The probability of obtaining 173 or more successen i (Round the final answer to two decimal places as needed Round all intermediate values to two decimal places as needed)

Answer 1

The mean and standard deviation is

$\mu =np=500\times 0.3=150$ and $\sigma =\sqrt{np(1-p)}=\sqrt{500\times 0.3(1-0.3)}\approx 10.25$

We now define the standard random variable Z as $z={X-150\over 10.25}$ where X is the number of success

Then the required probability is

P(X > 173) = P(X > 172.5) = P(z> 172.5 – 150 10.25 = P(Z > 2.20) = 0.0139

Hence the required probability after rounding is 0.01