# Normal curve approximation to the binomial distribution

10. Assume the distribution is normal. Use the area of the normal curve to answer the question. Round to the nearest whole percent.

The average size of the fish in a lake is 11.4 inches, with a standard deviation of 3.2 inches. Find the probability of catching a fish longer than 17 inches.

11. A company installs 5000 light bulbs, each with an average life of 500 hours, standard deviation of 100 hours, and distribution approximated by a normal curve. Find the approximate number of bulbs that can be expected to last more than 400 hours.

12. Suppose 500 coins are tossed. Using the normal curve approximation to the binomial distribution, find the probability of 265 heads or more.

13. Solve the problem using the normal curve approximation to the binomial distribution.

A multiple choice test consists of 60 questions. Each question has 4 possible answers of which one is correct. If all answers are random guesses, estimate the probability of getting at least 20% correct.

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#### Solution Preview

Please see the attachment.

Problem #10

The mean is m = 11.4 and the standard deviation is d = 3.2.

Let Y = (X - m) / d = (X - 11.4) / 3.2, then Y satisfies the standard normal distribution and we have X = 3.2Y + 11.4. Now we find

P(X > 17) = P(3.2Y + 11.4 > ...

#### Solution Summary

Normal curve approximation to the binomial distribution is assessed in the solution.