Ch. 6 Continuous Probability Distributions

uniform probability distribution

A continuous probability distribution for which the probability that the random variable will assume a value in any interval is the same for each interval of equal length.

exponential probability distribution

A continuous probability distribution that is useful in computing probabilities for the time it takes to complete a task.

normal probability distribution

A continuous probability distribution. Its probability density function is bell-shaped and determined by its mean and standard deviation .

probability density function

A function used to compute probabilities for a continuous random variable. The area under the graph of a probability density function over an interval represents probability.

continuity correction factor

A value of .5 that is added to or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution.

standard normal probability distribution

a normal distribution with a mean of zero and a standard deviation of one

14. In a standard normal distribution, the probability that Z is greater than zero is a. 0.5 b. equal to 1 c. at least 0.5 d. 1.96

a. 0.5

19. The uniform probability distribution is used with a. a continuous random variable b. a discrete random variable c. a normally distributed random variable d. any random variable, as long as it is not nominal

a. a continuous random variable

16. The uniform, normal, and exponential distributions are a. all continuous probability distributions b. all discrete probability distributions c. can be either continuous or discrete, depending on the data d. all the same distribution

a. all continuous probability distributions

38. A continuous random variable may assume a. all values in an interval or collection of intervals b. only integer values in an interval or collection of intervals c. only fractional values in an interval or collection of intervals d. all the positive integer values in an interval

a. all values in an interval or collection of intervals

4. A normal probability distribution a. can have any value of the mean b. must have a mean of 0 c. must have a standard deviation of 0 d. must have a standard deviation of 1 and a mean of 0

a. can have any value of the mean

37. A normal probability distribution a. is a continuous probability distribution b. is a discrete probability distribution c. can be either continuous or discrete d. must have a standard deviation of 1

a. is a continuous probability distribution

35. The mean of a standard normal probability distribution a. is always equal to zero b. can be any value as long as it is positive c. can be any value d. is always greater than zero

a. is always equal to zero

8. For any continuous random variable, the probability that the random variable takes avalue less than zero a. is any number between zero and 1 b. is more than 1, since it is contineous c. is a value larger than zero d. the random variable can't have a value less than zero

a. is any number between zero and 1

11. The probability that a continuous random variable takes any specific value a. is equal to zero b. is at least 0.5 c. depends on the probability density function d. is very close to 1.0

a. is equal to zero

23. In a standard normal distribution, the range of values of z is from a. minus infinity to infinity b. -1 to 1 c. 0 to 1 d. -3.09 to 3.09

a. minus infinity to infinity

21. For the standard normal probability distribution, the area to the left of the mean is a. -0.5 b. 0.5 c. any value between 0 to 1 d. 1

b. 0.5

30. The exponential probability distribution is used with a. a discrete random variable b. a continuous random variable c. any probability distribution with an exponential term d. an approximation of the binomial probability distribution

b. a continuous random variable

28. When a continuous probability distribution is used to approximate a discrete probability distribution, a value of 0.5 is a. added and/or subtracted from the area b. added and/or subtracted from the value of x c. added to the area d. subtracted from the area

b. added and/or subtracted from the value of x

17. A value of 0.5 that is added and/or subtracted from a value of x when the continuous normal distribution is used to approximate the discrete binomial distribution is called a. 50% of the area under the normal curve b. continuity correction factor c. factor of conversion d. all of the alternatives are correct answers

b. continuity correction factor

36. The standard deviation of a standard normal distribution a. is always equal to zero b. is always equal to one c. can be any positive value d. can be any value

b. is always equal to one

10. The center of a normal curve is a. always equal to zero b. is the mean of the distribution c. cannot be negative d. is the standard deviation

b. is the mean of the distribution

2. In a standard normal distribution, the a. mean and the standard deviation are both 1 b. mean is 0 and the standard deviation is 1 c. mean is 1 and the standard deviation is 0 d. mean and the standard deviation can have any value

b. mean is 0 and the standard deviation is 1

24. For a uniform probability density function, a. the height of the function cannot be larger than one b. the height of the function is the same for each value of x c. the height of the function is different for various values of x d. the height of the function decreases as x increases

b. the height of the function is the same for each value of x

15. A negative value of Z indicates that a. the number of standard deviations of an observation is to the right of the mean b. the number of standard deviations of an observation is to the left of the mean c. a mistake has been made in computations, since Z cannot be negative d. the data has a negative mean

b. the number of standard deviations of an observation is to the left of the mean

26. A uniform probability distribution is a continuous probability distribution where the probability that the random variable assumes a value in any interval of equal length is a. different for each interval b. the same for each interval c. at least one d. None of these alternatives is correct.

b. the same for each interval

41. For a standard normal distribution, the probability of z 0 is a. zero b. -0.5 c. 0.5 d. one

c. 0.5

33. Which of the following is not a characteristic of the normal probability distribution? a. symmetry b. The total area under the curve is always equal to 1. c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean d. The mean is equal to the median, which is also equal to the mode.

c. 99.72% of the time the random variable assumes a value within plus or minus 1 standard deviation of its mean

12. A normal distribution with a mean of 0 and a standard deviation of 1 is called a. a probability density function b. an ordinary normal curve c. a standard normal distribution d. none of these alternatives is correct

c. a standard normal distribution

13. The z score for the standard normal distribution a. is always equal to zero b. can never be negative c. can be either negative or positive d. is always equal to the mean

c. can be either negative or positive

34. For a normal distribution, a negative value of z indicates a. a mistake has been made in computations, because z is always positive b. the area corresponding to the z is negative c. the z is to the left of the mean d. the z is to the right of the mean

c. the z is to the left of the mean

25. The probability density function for a uniform distribution ranging between 2 and 6 is a. 4 b. undefined c. any positive value d. 0.25

d. 0.25

9. For the standard normal probability distribution, the area to the right of the mean is a. more than, 1 since the normal distribution has an upper bound of infinity b. 3.09 c. 1.96 d. 0.5

d. 0.5

39. A continuous random variable is uniformly distributed between a and b. The probability density function between a and b is a. zero b. (a - b) c. (b - a) d. 1/(b - a)

d. 1/(b - a)

40. If the mean of a normal distribution is negative, a. the standard deviation must also be negative b. the variance must also be negative c. a mistake has been made in the computations, because the mean of a normal distribution cannot be negative d. None of these alternatives is correct.

d. None of these alternatives is correct.

1. Which of the following is a characteristic of the normal probability distribution? a. The mean, median, and the mode are not equal b. The distribution is not symmetrical c. The standard deviation must be 0 d. The standard deviation must be 1

d. The standard deviation must be 1

22. Which of the following is not a characteristic of the normal probability distribution? a. The mean, median, and the mode are equal b. The mean of the distribution can be negative, zero, or positive c. The distribution is symmetrical d. The standard deviation must be 1

d. The standard deviation must be 1

20. For any continuous random variable, the probability that the random variable takes on exactly a specific value is a. 1.00 b. 0.50 c. any value between 0 to 1 d. almost zero

d. almost zero

5. A standard normal distribution is a normal distribution with a. a mean of 1 and a standard deviation of 1 b. a mean of 0 and a standard deviation of 0 c. any mean and a standard deviation of 1 d. any mean and any standard deviation

d. any mean and any standard deviation

6. The standard deviation of a normal distribution a. is always greater than zero b. is always 1 c. can be any value d. cannot be negative

d. cannot be negative

7. For a continuous random variable x, the height of the function at x is a. the probability at a given value of x b. 0.50, since it is the middle value c. a value less than zero d. named the probability density function f(x)

d. named the probability density function f(x)

27. The function that defines the probability distribution of a continuous random variable is a a. normal function b. uniform function c. either normal of uniform depending on the situation d. probability density function

d. probability density function

18. For a continuous random variable x, the probability density function f(x) represents a. the probability at a given value of x b. the area under the curve at x c. the area under the curve to the right of x d. the height of the function at x

d. the height of the function at x

42. The highest point of a normal curve occurs at a. one standard deviation to the right of the mean b. two standard deviations to the right of the mean c. approximately three standard deviations to the right of the mean d. the mean

d. the mean

3. For a normal distribution, a positive value of z indicates that a. all the observations must have had positive values b. the area corresponding to the z is either positive or negative c. the sample mean is smaller than the population mean d. the sample mean is larger than the population mean

d. the sample mean is larger than the population mean

32. Larger values of the standard deviation result in a normal curve that is a. shifted to the right b. shifted to the left c. narrower and more peaked d. wider and flatter

d. wider and flatter