Question

A national survey found that ​58% of adults ages​ 25-29 had only a cell phone and no landline. suppose that three 25-29-year-olds are randomly selected. complete parts a through c below.

Answer 1

This question requires calculating the probability of different outcomes for a group of 25-29-year-olds who have only a cell phone using the binomial probability formula. Potential selection bias must be considered due to the survey's contact method. The binomial probability formula includes factors such as the number of trials, success probability, and the binomial coefficient.

Step-by-step explanation:

Calculating Probability for 25-29 Year Olds with Only Cell Phones

The scenario involves a statistical probability question pertaining to adults aged 25-29 who only use a cell phone, with no landline. The national survey indicates that 58% of this demographic fits the description. When randomly selecting three individuals from this age group, we want to find various probabilities associated with this particular statistic.

To solve this, we'll employ the binomial probability formula, which is given by:

P(X=k) = (n choose k) * p^k * (1-p)^(n-k)

where:

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  n is the number of trials (in this case, 3 people).
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  k is the number of successes (individuals with only a cell phone).
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  p is the probability of success on any given trial (58% or 0.58).
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  (n choose k) is a binomial coefficient.

This approach will allow us to calculate the probability of all possible outcomes for the number of individuals who only have a cell phone out of the three selected.

For example, the probability that all three selected individuals only have a cell phone is calculated as follows:

P(X=3) = (3 choose 3) * 0.58^3 * (1-0.58)^0 = 1 * 0.58^3 * 1

This process will be repeated to calculate the probabilities for X=0, X=1, and X=2, each representing different scenarios of interest.

It is important to note that the accuracy of the statistical analysis can be influenced by selection bias, as the source of contact (landline vs. cell phone) can skew the representation of the population. Additionally, the preference for communication methods, such as texting over calls, especially among younger demographics, has implications for data collection and analysis.