Question

The probability of a defective steel rod is $0.01.$ Steel rods are selected at random. Find the probability that the first defect occurs on the ninth steel rod. Use the $TI-83+orTI-84$ calculator to find the answer.

Short answer

The probability that the first defect occurs on the ninth steel rod is$0.0865$

Step-by-step solution

Content Introduction

We are given,

The probability of a defective steel rod is $0.01$. Also, Steel rods are selected at random.

Content Explanation

Let X the number of steel tested until the first defective is found. Therefore, the sample size X takes on the values $0,1,2,3,.......$with the probability $p=0.01$

The probability of the defective steel rod is $0.01$and the geometric distribution it follows is:

$X~G(0.01)$

The probability that the first defector occurs at nineth steel rod is $P(X=9)$

To find the probability using$TI-83+$calculator follow the steps:

Press $1$and then press $2^{nd}$DISTR

Arrow down to geometpdf. Press Enter

Enter $(0.01,9)$

The results show

$P(X=9)=0.0865$