Statistics: Chapter 4 Review
he mean for the exponential distribution equals the mean for the Poisson distribution only when the former distribution has a mean equal to: (a) 1.0 (b) 0.5 (c) 0.25 (d) 2.0 (e) the means of the two distributions can never be equal
(a) 1.0
The mean of exponential distribution is given as __________
(a) 𝟏/𝜆
A larger standard deviation for a normal distribution with an unchanged mean indicates that the distribution becomes: (a) Narrower and more peaked (b) Flatter and wider (c) More skewed to the right(d) More skewed to the left(e) A change in the standard deviation does not change the shape of the distribution
(b) Flatter and wider
Which of the following is not a correct statement? (a) The exponential distribution describes the Poisson process as a continuous random variable (b) The mean of the exponential distribution is the inverse of the mean of the Poisson (c) The Poisson is a probability distribution for a discrete random variable while the exponential distribution is continuous (d) The area under the curve for an exponential distribution equal 1
(b) The mean of the exponential distribution is the inverse of the mean of the Poisson
Which of the following statements regarding the probability density function, f(x), of the uniform distribution is correct? (a) The height of the density function differs for different values of X (b) The density function increases as the values of X increase (c) The density function is roughly "bell-shaped" (d) The density function is constant for all values that X can assume (e) None of the above statements are true
(d) The density function is constant for all values that X can assume
Which of the following statement is not true for an exponential distribution with parameter λ? (a) Mean = 𝟏 𝝀 (b) Standard deviation = 𝟏 𝝀 (c) The distribution is completely determined once the value of λ is known (d) The area under the curve is equal to one (e) The distribution is a two-parameter distribution since the mean and standard deviation are equal
(e) The distribution is a two-parameter distribution since the mean and standard deviation are equal
For standard normal distribution, the value of mean is
0
The standard normal curve is symmetric about the value
0
For a standard normal distribution, the value of standard deviation
1
The area of a standard normal curve is
1
A standard normal distribution has which of the following properties? a) The mean the variance both equal 1 b) The mean is equal to the variance c) The mean is equal to 0 and the variance is 1 d) The mean is equal to the standard deviation
C) The mean is equal to 0 and the variance is 1
Normal Distribution is applied for
Continuous Random Distribution (CRD)
If x is a normal random variable with a 𝝁 =30 and a 𝝈 =5, the probability that 𝒙 is greater than 22 is associated with a z-score of −8. T/F
False
Let 𝑥 be a normal random variable with a mean of 80 and a standard deviation of 16. A z-score was calculated for 𝑥, and the z-score is 0.8. This means that the corresponding value of 𝒙 is 67. T/F
False
P (0 < z < 1.17) = 0.878999. T/F
False
Normal Distribution is also known
Gaussian Distribution
Normal Distribution is symmetric about
Mean
X is a Normal random variable and Z is a standard normal random variable. How do you convert X to Z?
Subtracting mean from X and divide by standard deviation.
A normally distributed data set has a mean of 100, and it is known that 30% of the values are greater than 140. The standard deviation of the normal distribution can be determined. T/F
True
For a normal distribution its mean, median, and mode are equal. T/F
True
Which of the following is not a characteristic of the normal distribution? a) It is a symmetrical distribution b) The mean is always zero c) It is a bell-shaped distribution d) The area under the curve is equal to one
b)The mean is always zero
Which of the following do the normal distribution and the exponential density function have in common?( a) Both are bell-shaped( b) Both are symmetrical distributions (c) Both approach zero as 𝒙 approaches infinity (d) All of the above are features common to both distributions
c) Both approach zero as 𝒙 approaches infinity
Which of the following is/are true regarding the normal distribution curve? a) It is symmetrical b) It is bell shaped c) It is asymptotic in that each end approaches the horizontal axis but never reaches it d) Its mean, median, and mode are located at the same point e) All of the above statements are true
e) All of the above statements are true
The shape of the normal curve depends on its
standard deviation
