Question

The probability that a birth in the United States is male during 2018 is 0.511. Suppose a random number generator from 1 to 1,000 is used as a statistical model to create simulated results for births in the United States during 2018. Suppose the numbers 1 to 511 represent a male birth in the United States during 2018 and 512 to 1,000 represent a female birth in the United States during 2018. Explain whether the following results are consistent with the model, and if not, explain the expected number of male births and the expected number of female births for 300

trials.

In 300
simulated trials, 171 of the births are female and 129 are male.

Answer 1

Explanation:

The probability that a birth in the United States is male during 2018 is 0.511. So there are slightly more males than females born.

In 300 simulated trials, 171 of the births are female and 129 are male. More females are born so it is not consistent with the model.

The expected number of male birth for 300 trials should be 300*0.511 = 153.

The expected number of female = 300-153 = 147