Question

Alyssa performed an experiment to measure the acceleration of a falling ball. She ran the experiment many times. Her results were distributed normally, with a mean of 9.75 meters per second and a standard deviation of 0.08 meters per second.

Alyssa can be 95% sure that her next measurement will fall between the values of
and
meters per second.

Answer 1

Answer:
The range of values that Alyssa can be 95% sure her next measurement will fall within is 9.59 to 9.91 meters per second

(Hope this helps)

Explanation:

Start with the mean: Alyssa's measurements have a mean of 9.75 meters per second.

Find the standard deviation: Alyssa's measurements have a standard deviation of 0.08 meters per second.

Determine the level of confidence: Alyssa wants to be 95% confident in her interval.

Calculate the margin of error: Using a table of z-scores, we find that for a 95% confidence interval, the z-score is approximately 1.96. We can multiply this by the standard deviation to find the margin of error:

Margin of error = 1.96 x 0.08 = 0.1568 meters per second

Calculate the lower and upper bounds of the interval: Subtract the margin of error from the mean to find the lower bound, and add it to the mean to find the upper bound:

Lower bound = 9.75 - 0.1568 = 9.59 meters per second

Upper bound = 9.75 + 0.1568 = 9.91 meters per second

Interpret the interval: Alyssa can be 95% sure that her next measurement will fall between 9.59 and 9.91 meters per second.