Probability The most important function in probabilityand statistics is the density function for the standard normaldistribution, which is the familiar bell-shaped curve. Thefunction is1f(x) =V2T(a) The area under this curve between x = -1 and x = 1represents the probability that a normal random vari-able is within 1 standard deviation of the mean. Find thisprobability.(b) Find the area under this curve between x = -2 andx = 2, which represents the probability that a normalrandom variable is within 2 standard deviations of themean.(c) Find the probability that a normal random variable is with-in 3 standard deviations of the mean.5/-

We will use Excel to find the required areas under the standard normal curve.

Answered: Probability The most important function…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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normal distribution has mean = 38 and sd= 4 (a) Find the z score corresponding to x = 28 (b) Find the z score corresponding to x = 45.
Data 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 4
A probability density curve is described by 2 line segments. The first connects (0, 1/7) and (3.5. 1/7), and the other connects (3.5, 1/7) to the x-axis. Part A: Sketch the probability density curve as described. (Be sure to label all values) Part B: Determine the x-value where the second segment crosses the x-axis. Part C: Determine P(X 0.05). Part E: Determine the median x-value of this distribution.
A random variable is normally distributed with a mean of μ = 50 and a standard deviation of a = 10. (a) The following figure shows that the normal curve almost touches the horizontal axis at three standard deviations below and at three standard deviations above the mean (in this case at 20 and 80). Areas Under the Curve for any Normal Distribution O O м-30 20 μ-20 30 40 20 40 60 Sketch a normal curve for the probability density function. Label the horizontal axis with values of 20, 30, 40, 50, 60, 70, and 80. 99.7% 95.4% μ-lo н 50 68.3% 60 μ + lo 70 80 A T μ + 20 80 70 50 30 +30 80 X 70 60 50 40 30 20 30 50 70 80 60 40 20 (b) What is the probability the random variable will assume a value between 20 and 80? (Round your answer to three decimal places.) (c) What is the probability the random variable will assume a value between 40 and 60? (Round your answer to three decimal places.)
A random variable X follows the continuous uniform distribution with a lower bound of -4 and an upper bound of 18. a. What is the height of the density function f(x)? (Round your answer to 4 decimal places.) f(x) 0.0455 b. What are the mean and the standard deviation for the distribution? (Round your answers to 2 decimal places.) Mean Standard deviation P(X ≤ -2) 7.00 6.35 c. Calculate P(X ≤-2). (Round intermediate calculations to at least 4 decimal places and final answer to 4 decimal places.)
Let x = red blood cell (RBC) count in millions per cubic millimeter of whole blood. For healthy females, x has an approximately normal distribution with mean ? = 3.6 and standard deviation ? = 0.6. (a) Convert the x interval, 4.5 < x, to a z interval. (Round your answer to two decimal places.) ____< z(b) Convert the x interval, x < 4.2, to a z interval. (Round your answer to two decimal places.)z < ____(c) Convert the x interval, 4.0 < x < 5.5, to a z interval. (Round your answers to two decimal places.) _____< z < ______(d) Convert the z interval, z < −1.44, to an x interval. (Round your answer to one decimal place.)x < ____(e) Convert the z interval, 1.28 < z, to an x interval. (Round your answer to one decimal place.) ____< x(f) Convert the z interval, −2.25 < z < −1.00, to an x interval. (Round your answers to one decimal place.)_____ < x < ____(g) If a female had an RBC count of 5.9 or higher, would that be considered unusually…
The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable X having the density function shown to the right. Find the variance of X (x-8). f(x)2-(X-8). 9sx< 10, 8
Significance For bone density scores that arc normally distributed with a mean of 0 and a standard deviation of I, find the percentage of scores that are a. significantly high (or at least 2 standard deviations above the mean). b. significantly low (or at least 2 standard deviations below the mean). c. not significant (or less than 2 standard deviations away from the mean).
The probability density function of the time it takes a hematology cell counter to complete a test on a blood sample is f(x) = 0.04 for 58 < x< 83 seconds. Round your answers to 2 decimal places. (a) What proportion of tests require more than 70 seconds to complete? i (b) What proportion of tests require less than one minute to complete? i (c) Determine the mean and variance of the time to complete a test on a sample. Mean = i seconds Variance = i seconds?
The proportion of people who respond to a certain mail-order solicitation is a continuous random variable X that has the density function (2x + 4 0 < x<1 f(x) = - 0, 5 elswhere Find the stàndard deviation of above stated continuous random variable (X)

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