Final Answer:
a) The average monthly household cellular phone bill is $100 and b) the probability that a randomly selected monthly cell phone bill is between $87 and $110 is 0.6826. So Option 1. $100; 0.6826 is correct.
Step-by-step explanation:
According to CBS Money Watch, the average monthly household cellular phone bill is $100. To determine the probability that a randomly selected monthly cell phone bill is between $87 and $110, we can use the empirical rule or the 68-95-99.7 rule for normal distributions.
The given range of $87 to $110 spans one standard deviation from the mean. For a normal distribution, approximately 68% of the data falls within one standard deviation of the mean. Therefore, the probability of a randomly selected monthly cell phone bill being between $87 and $110 is 0.6826 or 68.26%.
In mathematical terms, this probability is derived from the area under the normal distribution curve between the z-scores corresponding to $87 and $110. By standardizing the values using the formula z = (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation, we can find the z-scores for $87 and $110.
Using a standard normal distribution table, we can then determine the proportion of values falling between these z-scores. In this case, the probability is 0.6826, indicating that the majority of monthly cell phone bills are within one standard deviation of the average.
In summary, the average monthly household cellular phone bill is $100, and the probability of a randomly selected monthly cell phone bill falling between $87 and $110 is 0.6826, in line with the 68-95-99.7 rule for normal distributions.So Option 1. $100; 0.6826 is correct