A distribution is not symmetric if the tails on both ends of the density curve that represents it are close to identical. A. True B. False
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- A spinner contains the values 0 up to, but not including, 1. The outcomes of the spinner are equally likely, so the density curve is described by a uniform distribution as shown. Let X = the random number spun on the spinner. Height = 1 0 Random number What is the mean of X and the median of X? Mean = 0.25 Median = 0.5 Mean = 0.5 Median = : 0.5 Mean 0.75 Median 0.5 Mean = 0.5 Median = 0.25 Mean = 0.5 Median = 0.75 = -1. The region formed by a probability density function represented by a nonconstant linear function is _______________. a. Triangular b. Trapezoidal c. None of these d. Rectangular 2. The following is true about probability density function EXCEPT _______. a. The function is always nonnegative. b. None of these c. The probability of an individual value of random variable is zero. d. The total area under the graph is 1. 3. The region formed by the probability density function representing a continuous uniform distribution is ____________. a. Triangular b. Rectangular c. Slanted Line Segment d. Horizontal Line SegmentBelow is a graph of a normal distribution with mean u = -2 and standard deviation o = 3. The shaded region represents the probability of obtaining a value from this distribution that is between -5 and -0.5. 0.4- 0.3- 0.2- .1- -5 - 0.5
- Let x denote the lifetime (in thousands of hours) of a certain type of fan used in diesel engines. The density curve of x is as pictured below. 50 € (a) Shade the area under the curve corresponding to the probability that the lifetime is at least 25,000 hours. 0 00 24 25 24 50 (b) Shade the area under the curve corresponding to the probability that the lifetime exceeds 25,000 hours. 0 50 25 00 25 50 50 ⓇO⁰ 25 25 50 50 Ⓡ0⁰ Oo 26 26 50 50 CData are obtained on the location of incidents on a 12-kilometer-long bridge. The distribution of the distance along the bridge (in kilometers) where an incident occurs is depicted in the density curve below. 12 Distance (kilometers) along the bridge where an accident occurs 12 1. The probability of an incident that occurs in any 4 kilometers long bridge segment is always distributed over any 4-kilometer interval. A. 1/3, uniformly B. 1/3, not uniformly C. 1/6, uniformly D. 1/2, not uniformly To put it another way, the probability is 2. What is P(9 < X < 12)? 1 Same as P(2 < X < 5). 2. Same as P(2 s X < 5). 3. Same as P(2 < X < 5). 4. Same as P(2 < X < 5). A. 1 B. 1 and 2 C. 2, 3, and 4 D. 1. 2. 3, and 4Suppose we have a uniform density curve whose length is 2, what would the height of the density curve have to be? Write your answer in decimal form.
- Which statement(s) are true about density curves? Please select ALL that apply. A) It is always symmetric. B) It is always on or above the horizontal axis. C) The total area under a density curve (and above the horizontal axis) equals 1. D) A density curve represents the distribution of a discrete random variable.Which of the following correctly compares the tt-distribution and zz-distribution? A. For small sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. B. For large sample sizes, the density curve of the t-distribution is not symmetric, but the density curve of the z-distribution is symmetric. C. The curves of both distributions are symmetric, but the height of the density curve of the t-distribution is taller than the height of the density curve of the z-distribution. D. The area under the density curve of the t-distribution is greater than the area under the density curve of the z-distribution, especially for small sample sizes. E. The density curve of the t-distribution is more spread out than the density curve of the z-distribution, especially for small sample sizes.Which are the properties of the standard normal distribution. ( select that all apply) -The total area under the probability density curve is 1 -It is symmetric about the mean -the z score can not be negative -the density curve is a straight line
- Let x be the amount of time (in minutes) that a particular commuter will have to wait for atrain.Suppose that the distribution is uniform and ranges between 0 and 20 minutes.a. Draw the density curve for x.b. Find the value of the height.c. What is the probability that x is more than 8 minutes?d. What is the probability that x is between 7 and 15 minutes?e. Find the value of c for which P(x < c) = 0.7.25. Which of the following is true about the median of a continuous distribution? A. u is the 50™ percentile B. i is the 75" percentile C. The area under the density curve to the right of u is larger than the area to the left of u D. i satisfies F(u)=1Assume that the variable under consideration has a density curve. The area under the density curve that lies to the right of 20 is 0.368. a. What percentage of all possible observations of the variable exceed 20? b. What percentage of all possible observations of the variable are at most 20? a. ___________% (Type an integer or a decimal.) b. ___________% (Type an integer or a decimal.)