How Likely Is It That Adults Need Vision Correction?
What is the likelihood that adults need vision correction?
A survey sponsored by Vision Council revealed that 79% of adults require correction for their eyesight. If 20 adults are chosen at random, what is the probability that at least 19 of them need vision correction? Is 19 considered a significantly high number of adults in need of eyesight correction?
Probability of Adults Needing Vision Correction
The likelihood that at least 19 out of 20 randomly chosen adults require vision correction can be calculated using the binomial probability formula. Let's dive into the details!
To calculate the probability of at least 19 adults needing vision correction out of a group of 20, we can use the binomial probability formula. The formula for determining the probability of at least a certain number of successes in a fixed number of trials is:
P(X ≥ k) = 1 - P(X < k-1)
Where:
X is the number of individuals in need of vision correction,
k is the intended minimum value of individuals needing correction.
By applying this formula to our scenario, we want to find P(X > 19), which is equivalent to 1 - P(X < 18). Calculating the probabilities for each incremental value and summing them up using the binomial probability formula will give us the desired result.
Having 19 adults out of 20 needing vision correction is considered a significantly high number. It indicates a majority of the selected adults have eyesight issues that require correction, emphasizing the importance of regular eye check-ups and vision care.