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Answer :
Answer: a. If the 56% rate is correct, the expected number of smartphone users who use them in theaters would be 0.56 * 250 = 140. To find the probability of getting 122 or fewer, we would need to use the binomial distribution.
The binomial distribution model gives the probability of getting exactly r successes in n trials. The formula is:
P(X = r) = C(n, r) (p^r) ((1 - p)^(n - r))
where:
n is the number of trials (in this case, the number of adults surveyed, 250)
r is the number of successes (in this case, the number of adults who use their smartphones in theaters, 122)
p is the probability of success on each trial (in this case, the probability of an adult using their smartphone in theaters, 0.56)
C(n, r) is the number of combinations of n items taken r at a time.
However, to find the cumulative probability of getting 122 or fewer successes, we would have to add up the probabilities for each number of successes from 0 to 122. This can be a tedious calculation without a statistical calculator or software.
b. Whether the result of 122 is significantly low depends on the calculated probability. If the probability is less than 0.05 (a common threshold in statistics), then we could say that the result is significantly low.
As mentioned above, the calculation of the binomial distribution, especially for a cumulative probability, can be complex without a statistical calculator or software. It is recommended to use such a tool to get a precise result. Once you get the result, you can round to four decimal places as needed.
Step-by-step explanation:
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