Deck 8: Continuous Probability Distributions

Question 1

Given that Z is a standard normal variable, the value z for which P(Z $\le$ z) = 0.2580 is:

A) 0.70 .
B) 0.758 .
C) - 0.65 .
D) & 0.242 .

Answer 1

- 0.65 .

Question 2

Given that X is a normal variable, which of the following statements is (are) true? S

Answer 2

D

Question 3

If the random variable X is normally distributed with a mean of 75 and a standard deviation of 8, then P(X ≤ 75) is:

Answer 3

D

Question 4

What proportion of the data from a normal distribution is within 2 standard deviations of the mean?

Question 5

Which of the following is always true for all probability density functions of continuous random variables?

Question 6

Like the normal distribution, the exponential density function f(x):

Question 7

Given that the random variable X is normally distributed with a mean of 20 and a standard deviation of 7, P(28 $\le$ X $\le$ 30) is:

A) 2
B) 0.0507 .
C) 0.8729
D 0.9236

Question 8

Given that Z is a standard normal random variable, what is the value of Z if the area to the left of Z is 0.1949?

Question 9

If the continuous random variable X is uniformly distributed over the interval [15, 25], then the mean of X is:

Question 10

Given that Z is a standard normal random variable, P(-1.23 $\le$ Z $\le$ 1.89) is:

A) 0.1903 .
B) 0 . .9706 .
C) 0.8907 .
D) 0.7803 .

Question 11

If the random variable X is exponentially distributed with parameter = 4, then the probability P(X 0.25), up to 4 decimal places, is:

Question 12

Given that Z is a standard normal random variable, what is the value of Z if the area to the right of Z is 0.8212?

Question 13

If X is a normal random variable with a standard deviation of 10, then 3X has a standard deviation equal to:

Question 14

If Z is a standard normal random variable, then P(-2.28 $\le$ Z $\le$ -1.96 ) is:

A) 0.0250 .
B) 0.0146 .
C) - 0.0104 .
D) 0.0 .0104 .

Question 15

If the random variable X is exponentially distributed with parameter = 3, then P(X 2), up to 4 decimal places, is:

Question 16

What are the values of z that correspond to the P(-z $\le$ Z $\le$ z) equal to 0.4778?

A) $\pm 0.2389$ .
B) $\pm 0.71$ .
C) $\pm 0.64$ .
D) None of these choices are correct.

Question 17

Which of the following distributions is suitable to model the length of time that elapses before the first telephone call is received by a switchboard?

Question 18

If the random variable X is exponentially distributed with parameter $\lambda$ = 1.75, then P(1.5 $\le$ X $\le$ 3.8), up to 4 decimal places, is:

A) $0.0711 .$
B) $0.0473$ .
C) $0.1184 .$
D) $0.4739$ .

Question 19

Given that Z is a standard normal random variable, P(Z > − 2.68) is:

Question 20

A standard normal distribution is a normal distribution with:

Question 21

Find the value of σ if it is know that X is normally distributed with mean 5 and 14.92% of the values are above 8?

Question 22

The probability density function f(x) for a uniform random variable X defined over the interval [1, 11] is:

Question 23

Which of the following distributions is considered the cornerstone distribution of statistical inference?

Question 24

Which of the following distributions is not symmetrical?

Question 25

Which of the following is true for a normal distribution?

Question 26

If the random variable X is exponentially distributed, then which of the following statements best describes the mean of X?

Question 27

If Z is a standard normal random variable, the area between z = 0.0 and z =1.30 is 0.4032, while the area between z = 0.0 and z = 1.50 is 0.4332. What is the area between z = -1.30 and z = 1.50?

Question 28

The height of the function for a uniform probability density function f(x):

Question 29

The mean of the exponential distribution equals the mean of the Poisson distribution only when the former distribution has a mean equal to:

Question 30

The probability density function f(x) of a random variable X that is normally distributed is completely determined once the:

Question 31

The probability density function, f(x), for any continuous random variable X, represents:

Question 32

The expected value, E(X), of a uniform random variable X defined over the interval , is:

Question 33

Find the value of µ, if X is a normal random variable, with standard deviation 2, and 2.5% of the values are below 1?

Question 34

The probability density function f(x) of a random variable X that is uniformly distributed between a and b is:

Question 35

Which of the following is not true for a random variable X that is uniformly distributed over the interval $$a \leq x \leq b$$ ?

A) E ( X ) = ( a + b ) / 2
B) = $V(X)=(b-a)^{2} / 12$
C) $\sigma = ( b - a ) / 6$
D) f ( x ) = $\frac { 1 } { b - a } \text { if } a \leq x \leq b$

Question 36

Which of the following distributions is appropriate to measure the length of time between arrivals at a grocery checkout counter?

Question 37

If the random variable X is uniformly distributed between 40 and 60, then P(35 $\le$ X $\le$ 45) is:

A) 1.0 .
B) 0.5 .
C) 0.25 .
D) 0.0 .

Question 38

If the z-value for a given value x of the random variable X is z = 2.326, and the distribution of X is normal with a mean of 50 and a standard deviation of 5, to what x-value does this z-value correspond?

Question 39

Given that Z is a standard normal random variable, the area to the left of a value z is expressed as:

Question 40

The function f(x) that defines the probability distribution of a continuous random variable X is a:

Question 41

Suppose that the probability p of a success on any trial of a binomial distribution equals 0.80. For which value of the number of trials, n, would the normal distribution provide a good approximation to the binomial distribution?

Question 42

If the mean of an exponential distribution is 4, then the value of the parameter is:

Question 43

In the normal distribution, the total area under the curve is equal to one.

Question 44

In the exponential distribution, the value of x can be any of an infinite number of values in the given range.

Question 45

A continuous probability distribution represents a random variable having an infinite number of outcomes that may assume any number of values within an interval.

Question 46

Given that X is a binomial random variable, the binomial probability P(X $\le$ x) is approximated by the area under a normal curve to the left of:

A) x .
B) - x
C) x + 0.5 .
D) x - 0.5 .

Question 47

In the normal distribution, the curve is asymptotic but never intercepts the horizontal axis either to the left or right.

Question 48

In the normal distribution, the curve is skewed.

Question 49

If we standardise the normal curve, we express the original x values in terms of their number of standard deviations away from the mean.

Question 50

Which of the following is not true for an exponential distribution with parameter ?

Question 51

Given a binomial distribution with n trials and probability p of a success on any trial, a conventional rule of thumb is that the normal distribution will provide an adequate approximation of the binomial distribution if:

Question 52

A smaller standard deviation of a normal distribution indicates that the distribution becomes:

Question 53

Which of the following is a characteristic of a normal distribution?

Question 54

Given that Z is a standard normal random variable, the mean of Z is:

Question 55

Given that X is a binomial random variable, the binomial probability P(X x) is approximated by the area under a normal curve to the right of:

Question 56

In the normal distribution, the mean, median and mode are all at the same position on the horizontal axis since the distribution is symmetric.

Question 57

Given that Z is a standard normal random variable, a positive z value means that:

Question 58

Given that Z is a standard normal variable, the variance of Z:

Question 59

In the normal distribution, the flatter the curve, the larger the standard deviation

Question 60

Given that Z is a standard normal variable, the value z for which P(Z z) = 0.6736 is:

Question 61

Continuous probability distributions describe probabilities associated with random variables that are able to assume any of an infinite number of values.

Question 62

If the random variable X is exponentially distributed and the parameter of the distribution $\lambda$ = 4, then P(X $\le$ 0.25) = 0.3679.

Question 63

Using the standard normal curve, the z-score representing the 75th percentile is 0.75.

Question 64

Let z₁ be a z-score that is unknown but identifiable by position and area. If the area to the right of z₁ is 0.7291, the value of z₁ is -0.61.

Question 65

For a normal curve, if the mean is 20 minutes and the standard deviation is 5 minutes, the area to the right of 13 minutes is 0.9192.

Question 66

If the random variable X is exponentially distributed with $\lambda$ = 2 parameter, then the variance of the distribution is 0.5.

Question 67

For a normal curve, if the mean is 25 minutes and the standard deviation is 5 minutes, the area to the right of 25 minutes is 0.50.

Question 68

A random variable X is standardised when each value of X has the mean of X subtracted from it, and the difference is divided by the standard deviation of X.

Question 69

A random variable X is normally distributed with a mean of 250 and a standard deviation of 50. Given that X = 175, its corresponding z-score is -1.50.

Question 70

Using the standard normal curve, the z-score representing the 90th percentile is 1.28.

Question 71

Using the standard normal curve, the probability or area between z = -1.28 and z = 1.28 is 0.1003

Question 72

Given that z is a standard normal random variable, a negative value of z indicates that the standard deviation of z is negative.

Question 73

The mean of any normal distribution is always zero.

Question 74

Using the standard normal curve, the z-score representing the 10th percentile is 1.28.

Question 75

The mean and standard deviation of a normally distributed random variable that has been standardised are one and zero, respectively.

Question 76

The mean and the standard deviation of an exponential distribution are equal to each other.

Question 77

Let z₁ be a z-score that is unknown but identifiable by position and area. If the symmetrical area between -z₁ and + z₁ is 0.9544, the value of z₁ is 2.0.

Question 78

A random variable X is normally distributed with a mean of 150 and a variance of 25. Given that
X = 120, its corresponding z-score is 6.0.

Question 79

Using the standard normal curve, the area between z = 0 and z = 3.50 is about 0.50.

Question 80

The mean and standard deviation of an exponential random variable cannot equal to each other.