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A random sample of 81 automobiles traveling on a section of an interstate showed an average speed of 60 mph. The distribution of speeds of all cars on this section of highway is normally distributed, with a standard deviation of 13.5 mph. Refer to exhibit 8-3. If we are interested in determined an interval estimate for mu at 86.9% confidence the z value to use is 1.96 1.31 1.51 2.00 Refer to exhibit 8-3. The value to use for the standard error of the mean is 13.5 9 2.26 1.5 Refer to exhibit 8-3. The 86.9% confidence interval for mu is 46.500 to 73.500 57.735 to 62.265 59.131 to 60.869 50 to 70

Respuesta :

  1. The z value to use is 1.96.
  2. The value to use for the standard error of the mean is 2.26.
  3. The 86.9% confidence interval for mu is 59.131 to 60.869.

Probability can be used to make predictions or decisions in a variety of situations, such as in gambling, finance, and science. In these situations, probabilities can be calculated based on statistical data or by using mathematical models.

To find the confidence interval for the mean speed (mu) of all cars on this section of the highway, we can use the following formula:

Confidence interval for mu = sample mean +/- z * standard error of the mean

Where:

sample mean is the average speed of the 81 cars in the sample, which is 60 mph

z is the z-score corresponding to the desired confidence level. In this case, the desired confidence level is 86.9%, which corresponds to a z-score of 1.96.

standard error of the mean is the standard deviation of the sampling distribution of the mean, which is calculated as the standard deviation of the population divided by the square root of the sample size.

In this case, the standard error of the mean is 13.5 / sqrt(81) = 2.26 mph.

Plugging these values into the formula, we get:

Confidence interval for mu = 60 +/- 1.96 * 2.26 = 59.131 to 60.869

Therefore, at a confidence level of 86.9%, we can be confident that the interval between 59.131 and 60.869 mph includes the true mean speed of all cars on this section of the highway.

Learn more about probability, here https://brainly.com/question/11234923

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