Answer :
This calculation involves summing up the individual probabilities for each value of k from 0 to 114.
a. To find the probability of getting 114 or fewer smartphone owners who use them in theaters, we can use the binomial probability formula.
The formula is P(X ≤ k) = ∑ (n choose k) * p^k * (1-p)^(n-k), where n is the number of trials, k is the number of successful trials, and p is the probability of success.
In this case, n = 225 (the number of adults surveyed), k = 114 (the number of adults who use smartphones in theaters), and p = 0.58 (the probability of an adult using a smartphone in theaters).
Using this formula, we can calculate the probability as follows:
P(X ≤ 114) = ∑ (225 choose k) * 0.58^k * (1-0.58)^(225-k) for k = 0 to 114
b. To determine if the result of 114 is significantly low, we need to compare it to a certain threshold or criterion. This can be done by calculating the probability of getting a result as extreme as 114 or lower, assuming the 58% rate is correct.
If the probability is very low (typically less than 0.05 or 5%), it suggests that the result is statistically significant and unlikely to occur by chance. If the probability is higher, it indicates that the result may be within the range of expected variation.
Therefore, by comparing the probability calculated in part a to a significance level of choice, such as 0.05, we can determine if the result of 114 is significantly low or not.
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