Question

Out of 25 newborn babies of obese women, 10 weigh less than 2.5 kg. Find a 95%
confidence interval for the probability that the weight of a newborn baby of an
obese woman is less than 2.5 kg.

Answer 1

Answer on Question #54876 – Math – Statistics and Probability

Out of 25 newborn babies of obese women, 10 weigh less than 2.5 kg. Find a 95% confidence interval for the probability that the weight of a newborn baby of an obese woman is less than 2.5 kg.

Solution

$$\hat {p} = \frac {1 0}{2 5} = 0. 4.$$

A 95% confidence interval for the probability that the weight of a newborn baby of an obese woman is less than 2.5 kg is

$$\begin{array}{l} C I = \left(\hat {p} - z ^ {*} \sqrt {\frac {\hat {p} (1 - \hat {p})}{n}}; \hat {p} + z ^ {*} \sqrt {\frac {\hat {p} (1 - \hat {p})}{n}}\right) = \left(0. 4 - 1. 9 6 \sqrt {\frac {0 . 4 (1 - 0 . 4)}{2 5}}; 0. 4 + 1. 9 6 \sqrt {\frac {0 . 4 (1 - 0 . 4)}{2 5}}\right) \\ = (0. 2 0 8 0; 0. 5 9 2 0). \\ \end{array}$$

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