Carmen Homework 9 - Normal Distribution

Suppose X has a normal distribution with mean 10 and standard deviation 2. In order for the Z-score to be equal to 0, then X must be equal to

10

Where is the 10th percentile of the Z distribution?

-1.28

If the Z-score is 1.96, and X has a normal distribution with mean 60 and standard deviation 6, what X-value corresponds to this Z-score?

71.76

The Normal distribution is an example of a _________________ Distribution.

Continuous

The time (X) to complete a standardized exam is approximately normal with a mean of 70 minutes and standard deviation of 10 minutes. How much time should be given to complete the exam so that 80% of the students will complete the exam in the time given?

78.4 minutes

The time to complete a standardized exam is approximately normal with a mean of 70 minutes and a standard deviation of 10 minutes. The percentage of the students which take longer than 80 minutes to complete the exam is 84.13%.

False

For a normally distributed variable X with mean 40 and standard deviation 10, what is the probability that X equals exactly 30? In notation, what is P(X=30)?

0

What is the probability that a normally distributed random variable X is greater than 85 if μX = 75 and σX = 4?

0.006

X is a normally distributed random variable with mean 50 and standard deviation 5. What is the probability that 2X will be less than 110?

0.841

If an observation has a z-score of -1.5, how many standard deviations is it above or below the mean?

1.5 standard deviations below the mean