An experiment consists of 18 binomial trials, each having probability 2/3 of success. Use an approximating normal curve to estimate the following probabilities.

1. exactly 7 successes


2. between 9 and 13 successes, inclusive.

3. more than 12 successes.

in Algebra 1 Answers by

Your answer

Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
To avoid this verification in future, please log in or register.

1 Answer

Mean=18×⅔=12; SD=√(12(1-⅔))=2.

We use these values to apply to normal distribution. We are using a continuous distribution (normal) to approximate to a discreet distribution (binomial).

(1) For exact value X=7, we use the interval [6.5,7.5] to compute two Z scores, Z₁ and Z₂.

Z₁=(6.5-12)/2=-2.75; Z₂=(7.5-12)/2=-2.25.

p(-2.75)=0.0030; p(-2.25)=0.0122.

Difference is 0.009 or 0.9% approx. This is the normal approximation to the binomial distribution.

(2) Z₁=(8.5-12)/2=-1.75, Z₂=(13.5-12)/2=0.75. p(-1.75)=0.0401; p(0.75)=0.7734.

Difference is 0.7333, or 73.3% approx.

(3) Since 12 is the mean, it splits the distribution in half, so 50% will be 12 or above. But we need to work out what’s above, so we start at 12.5. Z=(12.5-12)/2=0.25. This corresponds to a probability of 59.9% approx.



by Top Rated User (816k points)

Related questions

0 answers
asked Apr 3, 2011 in Algebra 1 Answers by anonymous | 543 views
2 answers
asked Apr 28, 2014 in Word Problem Answers by anonymous | 208 views
1 answer
1 answer
asked Dec 13, 2017 in Algebra 1 Answers by dunbars Level 1 User (140 points) | 442 views
1 answer
asked Sep 16, 2017 in Word Problem Answers by lost child | 165 views
Welcome to, where students, teachers and math enthusiasts can ask and answer any math question. Get help and answers to any math problem including algebra, trigonometry, geometry, calculus, trigonometry, fractions, solving expression, simplifying expressions and more. Get answers to math questions. Help is always 100% free!
86,009 questions
91,923 answers
23,906 users