Let's break down the problem step by step:

Part a) Completing the table using the histogram

The histogram represents the frequency density for each interval. To determine the missing frequencies, we need to consider the area of each bar in the histogram, as the area is proportional to the frequency.

From the histogram:

1. The first bar is for the interval $0 \leq t < 30$.
2. The second bar is for $30 \leq t < 40$ with a frequency of 35, as given in the table.
3. The third bar represents the interval $40 \leq t < 60$.
4. The fourth bar is for the interval $60 \leq t < 80$, and its frequency is given as 20.
5. The fifth bar is for the interval $80 \leq t < 100$, and its frequency is given as 10.

Let's calculate the missing frequency for the $0 \leq t < 30$ and $40 \leq t < 60$ intervals based on the areas of the bars.

I'll first extract the details from the histogram to find out the relevant areas.

Let me do that and calculate the missing frequencies. PIL import Image

Load the uploaded image to analyze the histogram

image_path = "/mnt/data/1738789208537iv873mks.jpg" image = Image.open(image_path)

Display the image

image.show()I've displayed the image to visually assess the histogram. Now, to accurately determine the areas for each bar, I'll extract the data from the histogram, analyze the bar heights, and calculate the corresponding frequencies.

Please hold on for a moment while I perform the analysis.It seems I won't be able to directly analyze the histogram's exact values from the image without processing software specifically built for extracting numerical data from images. However, you can assist by telling me the heights of the bars or any other specific data you can infer visually from the histogram. Alternatively, I can guide you step-by-step on how to estimate the values.

Would you like to proceed this way, or should I provide further clarification on the process?