Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 145 hours. The company's research department takes a sample of 90 such tubes and finds that the mean life of these tubes is 2300 hours. What is the probability that this sample mean is within 22 hours of the mean life of all tubes produced by this company? Round your answer to four decimal places. P = i

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**Text Transcription for Educational Website:**

**Probability Problem: Electric Tube Lifespan Analysis**

Johnson Electronics Corporation manufactures electric tubes. It is known that the standard deviation of the lifespans of these tubes is 145 hours. The company's research department selects a sample of 90 such tubes, determining that the average lifespan of these tubes is 2300 hours.

Question: What is the probability that this sample mean is within 22 hours of the mean lifespan of all tubes produced by this company?

Please round your answer to four decimal places.

\[ P = \boxed{} \]

**Instructions:**
- Consider using statistical methods to solve the problem.
- Apply the properties of the normal distribution and standard error of the mean.
Transcribed Image Text:**Text Transcription for Educational Website:** **Probability Problem: Electric Tube Lifespan Analysis** Johnson Electronics Corporation manufactures electric tubes. It is known that the standard deviation of the lifespans of these tubes is 145 hours. The company's research department selects a sample of 90 such tubes, determining that the average lifespan of these tubes is 2300 hours. Question: What is the probability that this sample mean is within 22 hours of the mean lifespan of all tubes produced by this company? Please round your answer to four decimal places. \[ P = \boxed{} \] **Instructions:** - Consider using statistical methods to solve the problem. - Apply the properties of the normal distribution and standard error of the mean.
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