[APPLET] Milk Consumption You are performing a study about weekly per capita milk consumption. A previous study found weekly per capita milk consumption to be normally distributed, with a mean of 48.7 fluid ounces and a standard deviation of 8.6 fluid ounces. You randomly sample 30 people and record the weekly milk consumptions shown below.

a. Draw a frequency histogram to display these data. Use seven classes. Do the consumptions appear to be normally distributed? Explain.

Verified step by step guidance

1. Step 1: Organize the data into a frequency table. First, determine the range of the data by subtracting the smallest value (25) from the largest value (65). Divide this range into seven equal intervals (classes). Each interval should have the same width, calculated as (Range / Number of Classes).
2. Step 2: Count the number of data points that fall into each interval (class). This will give you the frequency for each class. For example, if the first interval is 25-34, count how many values in the dataset fall within this range.
3. Step 3: Draw the frequency histogram. On the x-axis, label the intervals (classes). On the y-axis, label the frequency (number of occurrences). For each interval, draw a bar whose height corresponds to the frequency of that interval.
4. Step 4: Analyze the shape of the histogram. Check whether the data appears to follow a bell-shaped curve, which is characteristic of a normal distribution. Look for symmetry and a peak near the mean (48.7 fluid ounces).
5. Step 5: Compare the histogram to the properties of a normal distribution. If the histogram is roughly symmetric and bell-shaped, the data can be considered approximately normally distributed. If there are significant skewness or multiple peaks, the data may not be normally distributed.

Key Concepts

Normal Distribution

Normal distribution is a probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean. It is characterized by its bell-shaped curve, defined by its mean and standard deviation. In this context, understanding normal distribution is crucial for analyzing the milk consumption data and determining if it follows this pattern.

Histogram

A histogram is a graphical representation of the distribution of numerical data, where the data is divided into intervals (or bins) and the frequency of data points in each interval is represented by the height of the bars. Creating a histogram for the milk consumption data will help visualize the distribution and assess its shape, which is essential for determining if the data appears normally distributed.

Sampling Distribution

The sampling distribution refers to the probability distribution of a statistic (like the sample mean) obtained from a large number of samples drawn from a specific population. In this case, understanding the sampling distribution is important because it allows us to make inferences about the population mean of milk consumption based on the sample of 30 individuals, especially in relation to the known mean and standard deviation.