6. Normal Distribution and Continuous Random Variables

Small Sample Weights of M&M plain candies are normally distributed. Twelve M&M plain candies are randomly selected and weighed, and then the mean of this sample is calculated. Is it correct to conclude that the resulting sample mean cannot be considered to be a value from a normally distributed population because the sample size of 12 is too small? Explain.

Which of the following does not describe the standard normal distribution?

Given the mean of a normal distribution is $\mu$ and the standard deviation is $\sigma$, what is the mean of the corresponding standard normal distribution after standardizing the variable?

For the standard normal distribution, what is the total area under the $N(0,1)$ normal curve?

Finding Area

In Exercises 23–36, find the indicated area under the standard normal curve. If convenient, use technology to find the area.

To the left of z=1.365

For the standard normal distribution, what proportion of the distribution lies between $z=-1.75$ and $z=1.75$?

For the standard normal distribution, what is the total area under the normal curve?

A random variable Z that is normally distributed with mean μ = 0 and standard deviation σ = 1 is said to have the ____________________.

For the standard normal probability distribution, what are the mean $\mu$ and standard deviation $\sigma$?

Student's $t$ distributions are symmetric about a value of $t$. What is that value?

Find the area under the standard normal distribution to the left of a z-score of $1.21$.

Find the area under the standard normal distribution to the right of a z-score of $-0.44$.

Find the area of the shaded region under the standard normal distribution.

Find the z-score such that $P$(Z < z)$=0.6331$.

Find the z-score corresponding to the probability/area shown under the standard normal curve below.