QuestionA survey showed that of adults need correction (eyeglasses, contacts, surgery, etc.) for their eyesight. If 20 adults are randomly selected, find the probability that no more than 1 of them need correction for their eyesight. Is 1 a significantly low number of adults requiring eyesight correction?
The probability that no more than 1 of the 20 adults require eyesight correction is 0.000 .
(Round to three decimal places as needed.)
Is 1 a significantly low number of adults requiring eyesight correction? Note that a small probability is one that is less than 0.05 .
A. No, because the probability of this occurring is not small.
B. No, because the probability of this occurring is small.
C. Yes, because the probability of this occurring is small.
D. Yes, because the probability of this occurring is not small.
Studdy Solution
STEP 1
1. The probability that an adult needs eyesight correction is .
2. The number of adults selected is .
3. We are using the binomial probability formula to find the probability of a specific number of successes in a fixed number of trials.
STEP 2
1. Define the binomial probability formula.
2. Calculate the probability of 0 adults needing correction.
3. Calculate the probability of 1 adult needing correction.
4. Sum the probabilities from steps 2 and 3.
5. Determine if the result is significantly low.
STEP 3
The binomial probability formula is given by:
where is the binomial coefficient, is the probability of success, and is the number of successes.
STEP 4
Calculate the probability that 0 adults need correction:
STEP 5
Calculate the probability that 1 adult needs correction:
STEP 6
Sum the probabilities from steps 2 and 3:
STEP 7
Determine if 1 is a significantly low number of adults requiring eyesight correction:
Since is less than 0.05, it is a significantly low probability.
Thus, the answer is:
C. Yes, because the probability of this occurring is small.
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