Exam 6: The Normal Probability Distribution

A random variable x is normally distributed with $\mu$ = 100 and $\sigma$ = 20. a. What is the median of this distribution? b. Find P(x median). c. Find P(x 75).

Which of the following characteristics is NOT a property of a normal distribution?

The total area under the curve f(x) of any continuous random variable x is equal to one.

A smooth frequency curve that describes the probability distribution of a continuous random variable is called a standard normal curve.

Which of the following correctly pertains to a continuous random variable?

The z-score of a random variable value of x = 2 is z = -2, while the standard deviation of the random variable x equals 2. What is the mean of x?

The z-score representing the 99th percentile of the standard normal curve is 3.0.

Textbook Narrative Twenty-five psychology instructors have formed a committee to pick next year's textbook, and they have narrowed their decision down to two equally good books, one with a better bibliography and references, and the other with a better format and illustrations. Since the books are considered to be equally good, we will assume the probability an instructor chooses either book is 0.5 and the instructors' decisions are made independently. -Refer to Textbook Narrative. Using the binomial distribution, find the probability 15 or more instructors choose the book with the better format and illustrations.

The random variable x is normally distributed, with a mean equal to 0.45 and a standard deviation equal to 0.40. What is the value of P(x 0.75)?

The market share of a relatively popular soft drink in Canada could be classified as a uniform random variable.

Even though the normal probability distribution deals with continuous variables, we can use it to approximate the binomial distribution whenever np > 5 and also nq > 5.

For some value of z, the probability that a standard normal variable is below z is 0.2090. What is the value of that z?

The Scholastic Aptitude Test (SAT) is a standardized test for college admissions in the United States. The mean SAT verbal score of next year's entering freshmen at the local college is 600. The college also knows 69.5% of the students scored less than 625. If the scores are normally distributed, what is the standard deviation of the SAT scores?

Let x be a continuous random variable and let c be a constant. Which of the following statements does NOT apply to the probability of x?

U.S. Presidential Election Narrative Do Americans tend to vote for the taller of the two candidates in a presidential election? In 30 presidential elections since 1856, 18 of the winners were taller than their opponents. Assume that Americans are not biased by a candidate's height and that the winner is just as likely to be taller or shorter than his opponent. Is the observed number of taller winners in the U.S. presidential elections unusual? -Refer to U.S. Presidential Election Narrative. Based on your answer to the previous question, can you conclude that Americans consider a candidate's height when casting their ballot?

Any continuous random variable cannot take on negative values.

Which of the following incorrectly describes both of the discrete probability distributions and the continuous probability density functions?

A random variable X is normally distributed with a mean of 150 and a variance of 36. Given that X = 120, then its corresponding z-score is 5.0.

Continuous random variables can assume values at all points on an interval, with no breaks between possible values.

If the mean, median, and mode are all equal for a continuous random variable, then the random variable must be normally distributed.