Question

determine whether the following graph can represent a variable with a normal distribution. explain your reasoning. if the graph appears to represent a normal distribution, estimate the mean and standard deviation. could the graph represent a variable with a normal distribution? explain your reasoning. select the correct choice below and, if necessary, fill in the answer boxes within your choice. a. no, because the graph is skewed left. b. no, because the graph is skewed right. c. no, because the graph crosses the x - axis. d. yes, the graph fulfills the properties of the normal distribution. the mean is approximately □ and the standard deviation is about □. (type whole numbers.)

Explanation:

Step1: Recall properties of normal distribution

A normal distribution is symmetric about the mean. The graph does not cross the x - axis (since the probability density function \(y = f(x)=\frac{1}{\sigma\sqrt{2\pi}}e^{-\frac{(x - \mu)^{2}}{2\sigma^{2}}}>0\) for all \(x\in(-\infty,\infty)\)). Also, it is not skewed (left - skewed or right - skewed).

Step2: Analyze the given graph

Since the graph is symmetric (assuming the general shape of a normal curve which is bell - shaped and symmetric), does not cross the x - axis (as per the formula of the normal probability density function \(y>0\) for all \(x\)), and is not skewed (left or right).

Answer:

D. Yes, the graph fulfills the properties of the normal distribution.