The proportion cars with number occupants within one standard deviation the mean

Solved Step by Step With Explanation- Calculate Proportion Within Range

Questions

For what proportion of cars was the number of occupants within one standard deviation of the mean? (Round the final answer to two decimal places.)

The proportion is 1.69

Step 1: Calculate the Mean (μ):

The mean is calculated by summing up the product of the number of occupants and their respective frequencies, and then dividing by the total number of cars.

N is the total number of cars

Calculating each part:

Step 2: Calculate the Standard Deviation (σ):

The standard deviation is calculated by summing up the squared differences between each number of occupants and the mean, multiplied by their respective frequencies. Then, divide by the total number of cars and take the square root.

f is the frequency of cars with that number of occupants

N is the total number of cars

σ = √76.751 / 100

σ ≈ √0.7675

Upper Limit = μ + σ = 1.45 + 0.876 ≈ 2.326

Cars with 1 or 2 occupants fall within this range (0.574 to 2.326).