Question

Im stuck on this:

the mean is 39.5 and standard deviation is 24.2
(d) Use the mean and standard deviation from part (b) as the parameters in the normal model to find the area under the normal curve between 350 and 370 feet. Compare this result to the relative frequency with which a home run distance between 350 and 369.9 feet is observed from the sample. The area under the normal curve between 350 and 370 feet is . The relative frequency with which a home run distance between 350 and 369.9 feet is observed from the sample is . These values close, which supports the conclusion that the normal model is a fit for the data. (Round to three decimal places as needed.)

Answer 1

To find the area under the normal curve for home run distances between 350 and 370 feet, the distances are converted to z-scores using the given mean and standard deviation, and then a Z-table is used to find the area. This value is compared to the actual sample data to determine if the normal model is a good fit.

Step-by-step explanation:

To calculate the area under the normal curve between 350 and 370 feet using the mean of 39.5 and standard deviation of 24.2, we first need to convert these values into z-scores. A z-score is determined by the formula (X - μ) / σ, where X is the value, μ is the mean, and σ is the standard deviation.

For X = 350, z = (350 - 39.5) / 24.2. For X = 370, z = (370 - 39.5) / 24.2. These z-scores allow us to use a Z-table to find the area to the left of each z-score. The area under the curve between 350 and 370 feet is the difference between these two areas.

To compare this to the relative frequency observed from the sample, we would need the actual sample data, which was presumably given in another part of the assignment. If the values are close, it supports the conclusion that the home run distances are normally distributed.