Final answer:
To determine if the four independent random variables are log normally distributed, we can perform a statistical test called the Shapiro-Wilk test.
Step-by-step explanation:
The question is asking whether four independent random variables are log normally distributed. To determine this, we need to consider the characteristics of log normal distributions and the properties of the random variables.
A log normal distribution is a type of continuous probability distribution where the logarithm of the random variable follows a normal distribution. If the four independent random variables are log normally distributed, it means that when we take the logarithm of each variable, the resulting distribution will be approximately normal.
To determine if the four independent random variables are log normally distributed, we can perform a statistical test called the Shapiro-Wilk test. This test assesses if a sample of data comes from a normal distribution. If the p-value of the test is greater than the significance level (0.05 in this case), we fail to reject the null hypothesis that the data is normally distributed.