Multiple Choice
In the (standard normal distribution), what happens to the graph of the normal curve as the mean increases while the standard deviation remains constant?
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6. Normal Distribution and Continuous Random Variables
Standard Normal Distribution
Multiple Choice
Which of the following is a similarity between the -distribution and the standard normal () distribution?
A
Both distributions are symmetric and bell-shaped.
B
Both distributions are only used when the population standard deviation is known.
C
Both distributions have the same variance for all sample sizes.
D
Both distributions are skewed to the right.
Verified step by step guidance1
Step 1: Understand the characteristics of the standard normal (z) distribution. It is symmetric, bell-shaped, has a mean of 0, and a standard deviation of 1. It is used when the population standard deviation is known.
Step 2: Understand the characteristics of the t-distribution. It is also symmetric and bell-shaped but has heavier tails than the normal distribution. It is used when the population standard deviation is unknown and the sample size is small.
Step 3: Compare the shapes of both distributions. Both are symmetric and bell-shaped, meaning they have the same general shape centered around their mean.
Step 4: Consider the variance of both distributions. The standard normal distribution has a fixed variance of 1, while the t-distribution's variance depends on the degrees of freedom and is generally larger for smaller sample sizes.
Step 5: Evaluate the options given in the problem. The correct similarity is that both distributions are symmetric and bell-shaped, while the other options are incorrect based on the properties of these distributions.
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