For this question, assume male and female babies are equally...

For this question, assume male and female babies are equally likely and ignore multiple births and intersex babies. A large city has two hospitals with maternity wards. Hospital A delivers an average of 231.2 babies a month and hospital B delivers an average of 432.6 babies a month. 1. Which of the hospitals is more likely to have more than 55% female babies in a given month? [ Select ] 2. Which of the hospitals is more likely to have exactly 50% female babies in a given month? [ Select ] 3. Which of the hospitals is more likely to have between 45% and 55% female babies in a given month? [ Select ]

Transcript

00:01 So for this problem, there actually is very little calculation that needs to be done.

00:05 If you understand the idea of a sampling distribution for proportions, then you actually are pretty much automatically almost at the end of the problem.

00:17 So we have that, pardon me, we're under the assumption that the population proportion of female babies would be 50%.

00:27 So the mean value of our sampling proportion, or our sampling distribution rather would be 0 .5.

00:35 The standard deviation of a distribution of sample proportions is always going to be equal to i'll write out the formula first here standard deviation of p hat pardon me p hat is going to be equal to the square root of p times 1 minus p divided by n so we can see that this is going to be inversely proportional to n and since we have p times 1 minus p and the population proportion would be 0 .5.

01:04 This would shake out to being simply 0 .5 over the square root of n.

01:11 For the first hospital, n, a, the number of babies they deliver per month is approximately 231 .2.

01:20 And for the second hospital, and b, they deliver more babies, 432 .6.

01:28 Now, since we have that the standard deviation is invertegradable.

01:31 Proportional to n, what that means is that the standard deviation for hospital a is going to be greater than the standard deviation for hospital b.

01:42 Well, what does that mean? that means that whenever we have a greater standard deviation, we're going to have more spread about the mean value.

01:55 So, for instance, we might have a is something like that, whereas b, its distribution is going to be much tighter...

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