Question

Suppose the mean of a normally distributed population is 300, and 200 simple random samples are drawn from the population. At

a 68% confidence level, (one standard deviation from the mean), about how many of the samples' confidence intervals would you
expect to contain the population mean?
O 64
O 96

Answer 1

the required number of samples to contain the population mean = 136

Explanation:

From the Empirical rule, If a data is normally distributed, then about 68% of the population lies within one standard deviation from mean.

Now, if we suppose that the mean of a normally distributed population is 300, and 200 simple random samples are drawn from the population. i.e. μ = 300

And;

Number of simple random samples: n = 200

Thus, by implication, we would expect about 68% of 200 samples confidence intervals to contain the population mean .

Hence,

Required number of samples = 68% of 200

This gives ;

0.68 x 200 = 136

Thus , the required number of samples = 136