Final answer:
(a) P(2)=0.28, (b) P(t;2)=0.72, and (c) P(25×55) requires additional distribution information to compute.
Step-by-step explanation:
To calculate the probabilities, we need to understand the information given.
Let:
P(2) be the probability of randomly selecting exactly 2 U.S. adults who are more likely to make purchases during a sales tax holiday.
P(t;2) be the probability of randomly selecting more than two (more than 2) U.S. adults who are more likely to make purchases during a sales tax holiday.
P(25×55) be the probability of randomly selecting between two and five (inclusive) U.S. adults who are more likely to make purchases during a sales tax holiday.
Given that 28% of U.S. adults say they are more likely to make purchases during a sales tax holiday, we can use this information to calculate the probabilities.
(a) P(2): The probability of selecting exactly 2 U.S. adults. This would be a specific number, so it is given directly as 28% or 0.28.
(b) P(t;2): The probability of selecting more than two U.S. adults. This would include 3 or more. Therefore,
P(t;2)=1−P(2) (complement rule).
P(t;2)=1−0.28=0.72
(c) P(25×55): The probability of selecting between two and five (inclusive) U.S. adults. This would be the sum of the probabilities of selecting 2, 3, 4, or 5 U.S. adults.
P(25×55)=P(2)+P(3)+P(4)+P(5)
Since we don't have specific probabilities for 3, 4, and 5 U.S. adults, we can't provide an exact calculation for
P(25×55) without that information. If you have additional information about the distribution, we can proceed with a more detailed calculation.
Otherwise, you might need to clarify the question or use an assumed distribution to estimate P(25×55).