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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

Expert verified

The probability that the first defect occurs on the ninth steel rod is0.0865

Step by step solution

01

Content Introduction

We are given,

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

02

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 0.01and 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 usingTI-83+calculator follow the steps:

Press 1and then press 2ndDISTR

Arrow down to geometpdf. Press Enter

Enter (0.01,9)

The results show

P(X=9)=0.0865

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