Questions: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 219 answered "none," 286 said "one," 364 said "two," 134 said "three," and 107 responded with four or more, A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05. P (four or more cell phones) = (Round to three decimal places as needed.) Is it unlikely for a household to have four or more cell phones in use? A. No, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05. B. No, because the probability of a respondent with four or more cell phones in use is greater than 0.05. C. Yes, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05. D. Yes, because the probability of a respondent with four or more cell phones in use is greater than 0.05.

In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 219 answered "none," 286 said "one," 364 said "two," 134 said "three," and 107 responded with four or more, A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05. P (four or more cell phones) = (Round to three decimal places as needed.) Is it unlikely for a household to have four or more cell phones in use? A. No, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05. B. No, because the probability of a respondent with four or more cell phones in use is greater than 0.05. C. Yes, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05. D. Yes, because the probability of a respondent with four or more cell phones in use is greater than 0.05.
Transcript text: In a survey of consumers aged 12 and older, respondents were asked how many cell phones were in use by the household. (No two respondents were from the same household.) Among the respondents, 219 answered "none," 286 said "one," 364 said "two," 134 said "three," and 107 responded with four or more, A survey respondent is selected at random. Find the probability that his/her household has four or more cell phones in use. Is it unlikely for a household to have four or more cell phones in use? Consider an event to be unlikely if its probability is less than or equal to 0.05 . $P$ (four or more cell phones) $=$ $\square$ (Round to three decimal places as needed.) Is it unlikely for a household to have four or more cell phones in use? A. No, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05 . B. No, because the probability of a respondent with four or more cell phones in use is greater than 0.05 . C. Yes, because the probability of a respondent with four or more cell phones in use is less than or equal to 0.05 . D. Yes, because the probability of a respondent with four or more cell phones in use is greater than 0.05 .
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Solution

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Solution Steps

Step 1: Calculate the Total Number of Respondents

To find the probability of households having four or more cell phones, we first need to calculate the total number of respondents. This is done by summing the number of respondents in each category:

\[N = n_0 + n_1 + n_2 + n_3 + n_{4+} = 219 + 286 + 364 + 134 + 107 = 1110\]

Step 2: Calculate the Probability of the Specific Outcome

The probability of a household having four or more cell phones is calculated by dividing the number of respondents indicating 'four or more' by the total number of respondents:

\[P(\text{four or more cell phones}) = \frac{n_{4+}}{N} = \frac{107}{1110} = 0.096\]

Step 3: Determine if the Event is Unlikely

Since the probability of having four or more cell phones is 0.096, which is greater than 0.05, the event is not considered unlikely.

Final Answer:

The probability of a household having four or more cell phones is 0.096. This event is not unlikely based on the given threshold of 0.05.

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