Problem

A recent survey found that $72 \%$ of all adults over 50 own cell phones. You randomly select 100 adults over 50 , and ask if he or she owns a cell phone. Shape: Since $n p(1-p)=$ , the shape is

Solution

Step 1 :This is a binomial distribution problem, where n=100 (the number of trials), and p=0.72 (the probability of success on each trial).

Step 2 :The mean and variance of a binomial distribution can be calculated using the formulas np and np(1-p) respectively.

Step 3 :Substitute n = 100 and p = 0.72 into the formulas.

Step 4 :The mean number of adults over 50 who own cell phones in a sample of 100 is \(100 * 0.72 = 72.0\)

Step 5 :The variance is \(100 * 0.72 * (1 - 0.72) = 20.16\)

Step 6 :Final Answer: The mean number of adults over 50 who own cell phones in a sample of 100 is \(\boxed{72.0}\) and the variance is \(\boxed{20.16}\).

From Solvely APP
Source: https://solvelyapp.com/problems/20313/

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