Question

a survey finds that customers are overcharged by price scanning systems, on average, on 1.95% of items. suppose a customer purchases 10 items. find the following probability.
a customer is not overcharged for any item.
the probability is 0.730153
(round to four decimal places as needed.)

Explanation:

Step1: Identify the probability of not being overcharged for one item

The probability of being overcharged for an item \(p = 0.0195\). So the probability of not being overcharged for one item \(q=1 - p=1 - 0.0195 = 0.9805\)

Step2: Use the binomial probability formula for \(n = 10\) and \(k = 0\)

The binomial probability formula is \(P(X=k)={n\choose k}p^{k}q^{n - k}\). Here \(n = 10\), \(k = 0\), \(p = 0.0195\), \(q = 0.9805\)

$$
LATEXBLOCK0
$$

Calculate \((0.9805)^{10}\approx0.730153\)

Answer:

\(0.7302\) (rounded to four decimal places)