Binomial Distributions Under ordinary circumstances: For all babies born in the entire global population, the proportion of male births tends to be consistently a bit higher, than the proportion of female births (Source: WHO - World Health Organization). In fact: For a randomly sampled individual birth from the global population, the probability that the baby's sex will be male is approximately 51.22%. Imagine that we will randomly record the sex outcome at birth for 25 future individual babies from the global population. We will let random variable X stand for the total number of male births in our sample. In this scenario, what is the numerical value of E(X)? Round to one digit past the decimal point, and state just the number part of your answer (no units). _______________________ In this same scenario: What is the numerical value of SD(X)? Round to one digit past the decimal point, and state just the number part of your answer (no units). _________________________ In this same scenario: What is the approximate value of P(X≤11) ? Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Binomial Distributions
Under ordinary circumstances: For all babies born in the entire global population, the proportion of male births tends to be consistently a bit higher, than the proportion of female births (Source: WHO - World Health Organization).
In fact: For a randomly sampled individual birth from the global population, the probability that the baby's sex will be male is approximately 51.22%.
Imagine that we will randomly record the sex outcome at birth for 25 future individual babies from the global population.
We will let random variable X stand for the total number of male births in our sample.
In this scenario, what is the numerical value of E(X)?
Round to one digit past the decimal point, and state just the number part of your answer (no units).
In this same scenario:
What is the numerical value of SD(X)?
Round to one digit past the decimal point, and state just the number part of your answer (no units).
In this same scenario:
What is the approximate value of P(X≤11) ?
Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).
In this same scenario:
What is the approximate value of P(X>11) ?
Write your answer as a percentage value, and round to three digits after the decimal point. Include a percent symbol after your answer (no spaces).
For all problems:
- Note that here, we have X~B(25, 51.22%)
- Assume that all individual baby births, and whether the sex of the baby is male or female, are all independent
events - Use the free online software GeoGebra (or any other accurate software that you like)
Problems 1 and 2:
- Show just the number part of your answer (don't also write any units, such as "babies" or "males", etc.)
- Show the value as just a decimal number (not a percentage value)
- Round to one digit past the decimal point
- Remember to follow the information shown in the accompanying instructional video
Problems 3 and 4:
- Show your answer value in percentage form
- Round to three digits past the decimal point
- Remember what the different inequality symbols mean (for instance, using the symbol < versus using ≤ , etc.)
- Remember to follow the information shown in the accompanying instructional video
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