In a city, 20% of the workers have incomes over $40,000 per year. A researcher chooses 1600 workers at random (with replacement) and finds that the mean is 320 and standard deviation is 16. what is the chance that between 320 and 336 of those have incomes over $40,000 per year?
To find the probability that between 320 and 336 out of 1600 workers have incomes over $40,000 per year, we can use the concept of the normal distribution.
First, let's calculate the mean and standard deviation of the sampling distribution. The mean of the sampling distribution is equal to the mean of the original population, which is 320. The standard deviation of the sampling distribution is equal to the standard deviation of the original population divided by the square root of the sample size. The standard deviation of the original population is 16, and the sample size is 1600. Therefore, the standard deviation of the sampling distribution is 16/sqrt(1600) = 16/40 = 4.
Next, we need to determine the z-scores corresponding to the values of 320 and 336. The z-score is calculated using the formula: z = (x - μ) / σ, where x is the value, μ is the mean, and σ is the standard deviation.
For the lower value of 320, the z-score is (320 - 320) / 4 = 0. For the upper value of 336, the z-score is (336 - 320) / 4 = 4.
Now, we can use a standard normal distribution table or a calculator to find the probability associated with these z-scores. The probability that the number of workers with incomes over $40,000 per year falls between 320 and 336 out of 1600 workers is equal to the area under the curve between the z-scores of 0 and 4.
Using a standard normal distribution table or a calculator, we find that the probability for this range is approximately 0.3520, or 35.20%.
Therefore, there is approximately a 35.20% chance that between 320 and 336 workers out of the randomly selected 1600 workers have incomes over $40,000 per year.
On Monday I wrote about an interview with a paleoanthropologist who referred to humans as a “very particular type of ape” and called us an “invasive species.” In that blog, I noted that this view of mankind has consequences. And one of those consequences is the “anti-natalist” movement we see becoming increasingly popular in the West as people are urged not to have children for the sake of the planet (among other reasons). And a recent article perfectly highlights my point.
The New Yorker published a review of two books, The Quickening and The Parenthood Dilemma, both of which “consider the ethics of procreation in the age of man-made climate change.” Indeed, the review was titled “The Morality of Having Kids in a Burning, Drowning World.” Here are just a few quotes from the fairly lengthy article:
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“Should I have a child, their greenhouse gas emissions will cause roughly fifty square meters of sea ice to melt every year that they are alive,” Rush writes. “Just by existing, they will make the world a little less livable for everyone, themselves included.”
. . . a growing body of commentary that debates the morality and ethics of procreation in this burning, drowning world. “It seems increasingly clear,” Crist continues, “that we are living in a time of radical destabilisation of life on Earth which complicates the act of bearing children in ways that society has yet to grapple with.”
Perhaps having a child under any circumstances, given the unimaginably high emotional, financial, ecological, and existential stakes, is an act of outrageous presumption.
Across the West, birth rates are plunging, dropping to new lows every year. Now, despite all the hype about the supposed climate and population crises, the book review notes, “In a 2021 Pew survey of childless adults who say they likely will not have children, only five per cent specifically named climate change as the crucial factor, with an additional nine per cent citing ‘the state of the world.’” So only a small percentage of childless adults are likely to remain childless because of the environment. But, interestingly, a 2023 Morning Consult poll of parents in five countries found “among people who already have kids, more than half say that climate anxiety does influence how many children they plan to have.”
But should we be anxious about the climate and not have children (or have fewer children) in an effort to keep the world “livable for everyone”? No! Twice, God has commanded mankind to be fruitful and multiply and fill the earth.
Be fruitful and multiply and fill the earth and subdue it. (Genesis 1:28)
And you, be fruitful and multiply, increase greatly on the earth and multiply in it. (Genesis 9:7)
Scripture teaches that children are a blessing from the Lord—they are a good thing!
And Scripture teaches that children are a blessing from the Lord—they are a good thing! Really, the whole anti-natalist movement is motivated by pride. In his arrogance, mankind assumes he knows enough about our extremely complex climate (even when past predictions have been wrong over and over again) to control the climate and that he knows better than God and therefore not only doesn’t but shouldn’t obey God’s command to “be fruitful and multiply.” This is man being his own god as the devil tempted in Genesis 3:5.
Instead of arrogantly assuming we know more than God, as humans we must humble ourselves, acknowledge our limitations, and have wise dominion over creation for our good and God’s glory. And all that starts with having a biblical worldview of mankind, children, this earth, and our Creator God.