The question is incomplete! Complete question along with Answer and step by step explanation is provided below.
Question:
Considering the three hypothetical scenarios from your lab activity: A. The typical amount of sleep per day for very young babies has a bell-shaped distribution with a mean of 18 hours and a standard deviation equal to 1 hours. B. The number of hours spent playing video games per week for gamers in the US has a bell-shaped distribution with a mean of 7 hours and a standard deviation equal to 2 hours. C. Car and truck speeds at a particular location have approximately a bell-shaped distribution with mean = 65 mph and standard deviation = 5 mph.
Match the curves from your lab activity to these scenarios
Gray curve = _____
Blue curve = _____
Green curve = _____
The curves of these normal distribution are attached as image.
Answer:
Gray curve = B
Blue curve = A
Green curve = C
Step-by-step explanation:
A Normal distribution can be defined by two parameters;
1. Mean (μ)
2. Standard deviation (σ)
In a normal distribution, the bulk of the values are concentrated around the mean and as we go left and right from the mean, the probability of that number occurring decreases.
A low value of standard deviation indicates that there are less variations hence the density at the mean would be large.
A higher value of standard deviation indicates that there are greater variations hence the density at the mean would be low and density would be greater at the tails.
Lets analyze each of the option.
Option A:
μ = 18 hours
σ = 1 hours
As you can see option A has the lowest standard deviation among all the options which suggests that the density at the mean would be greater than rest so we should expect a taller curve with very less wider curve.
The Blue curve best matches this description.
Option B:
μ = 7 hours
σ = 2 hours
As you can see option B has the a greater standard deviation than option A but less than option C which suggests that the density at the mean would be less than option A but greater than option C so we should expect less taller curve than option A and a more wider curve than option A.
The Gray curve best matches this description.
Option C:
μ = 65 mph
σ = 5 mph
As you can see option C has the greatest standard deviation among all options which suggests that the density at the mean would be very less and greater at the tails so we should expect least taller curve and most wider curve.
The Green curve best matches this description.
