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Answer :
a. The probability of fewer than half of 50 adults watching news videos can be estimated using a normal approximation by calculating the z-score based on the population proportion of 0.56.
b. For a sample of 250 adults, the same normal approximation can be applied to determine the probability of fewer than half watching news videos by calculating the z-score and referring to the standard normal distribution.
a. The probability that fewer than half in a sample of 50 adults will watch news videos, given a population proportion of 0.56, can be estimated using the normal approximation. The conditions for normal approximation are satisfied since both np (28) and n(1-p) (22) are greater than 10. By calculating the z-score using the formula z = (x - np) / sqrt(np(1-p)), where x is the number of adults watching news videos, we can find the corresponding probability using a standard normal distribution table or calculator.
b. When taking a sample of 250 adults, the same normal approximation can be applied since the conditions for approximation are met (np = 140 > 10 and n(1-p) = 110 > 10). The probability of fewer than half in the sample watching news videos can be determined by calculating the z-score and referencing the standard normal distribution.
Learn more about central limit theorem here: brainly.com/question/898534
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