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.
To determine if the given results are consistent with the model, we need to compare them to the expected number of male and female births based on the given probability.
Given that the probability of a birth being male is 0.511, and assuming the random number generator is unbiased and equally likely to generate any number from 1 to 1,000, we can calculate the expected number of male births and female births for 300 trials.
Expected number of male births = Probability of male birth * Total number of trials
= 0.511 * 300
= 153.3 (approximately)
Expected number of female births = Total number of trials - Expected number of male births
= 300 - 153.3
= 146.7 (approximately)
Comparing the expected numbers to the given results:
- In the given results, the number of female births is 171, which is greater than the expected number of 146.7.
- In the given results, the number of male births is 129, which is smaller than the expected number of 153.3.
Based on these comparisons, it appears that the given results are not consistent with the model. There is an excess of female births and a deficit of male births compared to what would be expected based on the given probability.
Therefore, the expected number of male births for 300 trials is approximately 153.3, and the expected number of female births is approximately 146.7.