A company manufactures tennis balls. When its tennis balls are dropped onto a concrete surface from a height of 100 inches, the company wants the mean height the balls bounce upward to be 55.2 inches. This average is maintained by periodically testing random samples of 25 tennis balls. If the t-value falls between -to 95 and to 95, then the company will be satisfied that it is manufacturing acceptable tennis balls. A sample of 25 balls is randomly selected and tested. The mean bounce height the sample is 56.8 inches and the standard deviation is 0.25 inch. Assume the bounce heights are approximately normally distributed. Is the company making acceptab tennis balls? Find -to 95 and to.95- -to.95 = to.95 = (Round to three decimal places as needed.)

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### Quality Control of Tennis Balls

A company manufactures tennis balls and evaluates their quality based on bounce height. When tested by dropping them onto a concrete surface from a height of 100 inches, the company aims for the balls to bounce to an average of 55.2 inches. This standard is checked regularly by selecting random samples of 25 tennis balls. 

The company considers its products acceptable if the t-value of the sample mean falls between \(-t_{0.95}\) and \(t_{0.95}\).

**Sample Testing:**
- A random sample of 25 balls was tested.
- The sample's mean bounce height was 56.8 inches.
- The standard deviation of the bounce heights is 0.25 inches.

**Objective:**
- Calculate \(-t_{0.95}\) and \(t_{0.95}\) to determine if the current batch meets the quality standards.

**Calculation Instruction:**
- Round results to three decimal places.

This process ensures that the balls consistently meet performance expectations, assuming the bounce heights are approximately normally distributed.
Transcribed Image Text:### Quality Control of Tennis Balls A company manufactures tennis balls and evaluates their quality based on bounce height. When tested by dropping them onto a concrete surface from a height of 100 inches, the company aims for the balls to bounce to an average of 55.2 inches. This standard is checked regularly by selecting random samples of 25 tennis balls. The company considers its products acceptable if the t-value of the sample mean falls between \(-t_{0.95}\) and \(t_{0.95}\). **Sample Testing:** - A random sample of 25 balls was tested. - The sample's mean bounce height was 56.8 inches. - The standard deviation of the bounce heights is 0.25 inches. **Objective:** - Calculate \(-t_{0.95}\) and \(t_{0.95}\) to determine if the current batch meets the quality standards. **Calculation Instruction:** - Round results to three decimal places. This process ensures that the balls consistently meet performance expectations, assuming the bounce heights are approximately normally distributed.
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