Question

1. in a batch of 1160 calculators, 5 were found to be defective. what is the probability that a calculator chosen at random will be defective? write the probability as a percent. round to the nearest tenth of a percent if necessary. 99.6% 0.4% 74.7% 0.5%

Explanation:

Step1: Calculate the probability formula

The probability \(P\) of an event is given by \(P=\frac{\text{Number of favorable outcomes}}{\text{Total number of outcomes}}\). Here, the number of favorable outcomes (defective calculators) is \(n = 5\), and the total number of outcomes (total calculators) is \(N=1160\). So, \(P=\frac{5}{1160}\).

Step2: Convert the fraction to a percentage

To convert the fraction \(\frac{5}{1160}\) to a percentage, we use the formula \(P(\text{percentage})=\frac{5}{1160}\times100\%\).

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Step3: Round to the nearest tenth of a percent

Rounding \(0.431\%\) to the nearest tenth of a percent. Since the second - decimal digit \(3<5\), we get \(0.4\%\).

Answer:

\(0.4\%\)