PART A: APPLYING THE NORMAL DISTRIBUTION P( z < -1.42) P( z > -2.17) P(z >...
PART A: APPLYING THE NORMAL DISTRIBUTION
- P( z < -1.42)
- P( z > -2.17)
- P(z > 2.35)
- P(-2.33 < z < 1.84)
- 2010 MCAT exam scores are normally distributed with a mean score of 25 with a standard deviation of 6.4
- What proportion of students had an MCAT score over 30?
- What proportion of students had scores less than 40?
- For model year 2010 vehicles the combined city/hwy gas mileage is approximately normal with a mean of 20.3 mpg and a standard deviation of 4.3 mpg.
- The 2010 Chevy Camaro gets 19 mpg. What percentage of other 2010 vehicles get better mpg than the Camaro?
- How low must a 2010 vehicle’s gas mileage be to fall in the lowest 10% of all vehicles?
- What gas mileage would a vehicle have to exceed to be in the top 8% of all 2010 vehicles?
Homework Answers
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PART A: APPLYING THE NORMAL DISTRIBUTION
P( z < -1.42)
P( z > -2.17)
P(z >...
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a)...
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a) Find P(Z > 0.45). b) Find P(0.7 SZ 1.6). c) Find 20.09. d) Find the Z-score for having area 0.18 to its left under the standard normal curve. e) Find the value of z such that P(-2SZS2) -0.5. 3. (4 points) The scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. a) Find the proportion...
6. Area under the normal distribution The following figure shows the normal distribution with the proportion...
6. Area under the normal distribution The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (u) plus three standard deviations (+30). Also, because the normal distribution is symmetrical,...
(3 points) In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency...
(3 points) In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg The 2008 Chevrolet Malibu with a four-cylinder engine has combined gas mileage...
- What proportion of a normal distribution is located between each of the following Z-score boundaries?...
What proportion of a normal distribution is located between each of the following Z-score boundaries? a. z= -0.50 and z= +0.50 b. z=-0.90 and z= +0.90 c. z=-1.50 and z= 1.50 For a normal distribution with a mean of μ = 80 and a standard deviation of σ= 20, find the proportion of the population corresponding to each of the following. a. Scores greater than 85. b. Scores less than 100. c. Scores between 70 and 90. IQ test scores are standardized to produce a normal distribution with...
Question 3: Consider the Standard Normal Distribution with mean 0 and standard deviation 1. Find the...
Question 3: Consider the Standard Normal Distribution with mean 0 and standard deviation 1. Find the following. a) P (z>0.5) b) P(z 1.5) c) P (-0.49 < z1.5) Question 4: If you have a normal distribution with mean 14 and standard deviation of 2. What is P(x >16)? Question 5 Professor Hardy assumes the exam scores are normally distributed and wants to grade "on a curve." The mean score was 68, with a standard deviation of 9, If he wants...
Standard Normal distribution. With regards to a standard normal distribution complete the following: (a) Find P(Z...
Standard Normal distribution.
With regards to a standard normal distribution complete the following: (a) Find P(Z > 0), the proportion of the standard normal distribution above the z-score of 0. (b) Find P(Z <-0.75), the proportion of the standard normal distribution below the Z-score of -0.75 (c) Find P(-1.15<z <2.04). (d) Find P(Z > -1.25). (e) Find the Z-score corresponding to Pso, the 90th percentile value.
6. Properties of the normal curve Aa Aa The following figure shows the normal distribution with...
6. Properties of the normal curve Aa Aa The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (H) plus three standard deviations (+30). Also, because the normal distribution...
(3.37) NOTE: The numerical values in this problem have been modified for testing purposes In its...
(3.37) NOTE: The numerical values in this problem have been modified for testing purposes In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles, There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.8 miles per gallon (mpg) and standard deviation 5.2 mpg. The...
1. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a. What ...
all questions. Do not round
answers
1. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a. What percentage of scores is between 55 and i 15? b. In a group of 20,000 randomly selected individuals, how many have an IQ score of 130 or more? 2. A Honda Civic has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 33 mpg and a standard deviation of...
9. (15.24) The length of human pregnancies from conception to birth varies according to a distribution...
9. (15.24) The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. The probability that the average pregnancy length for 6 randomly chosen women exceeds 270 days is about a 0.40. b 0.27. c 0.07. 10. (15.12) The gypsy moth is a serious threat to oak and aspen trees. A state agriculture department places traps throughout the state to detect the moths. When...
1. (5 points) Suppose Z is a random variable that follows the standard normal distribution. a) Find P(Z > 0.45). b) Find P(0.7 SZ 1.6). c) Find 20.09. d) Find the Z-score for having area 0.18 to its left under the standard normal curve. e) Find the value of z such that P(-2SZS2) -0.5. 3. (4 points) The scores on a test are normally distributed with a mean of 75 and a standard deviation of 8. a) Find the proportion...
6. Area under the normal distribution The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (u) plus three standard deviations (+30). Also, because the normal distribution is symmetrical,...
(3 points) In its Fuel Economy Guide for 2008 model vehicles, the Environmental Protection Agency gives data on 1152 vehicles. There are a number of outliers, mainly vehicles with very poor gas mileage. If we ignore the outliers, however, the combined city and highway gas mileage of the other 1120 or so vehicles is approximately Normal with mean 18.7 miles per gallon (mpg) and standard deviation 4.3 mpg The 2008 Chevrolet Malibu with a four-cylinder engine has combined gas mileage...
Question 3: Consider the Standard Normal Distribution with mean 0 and standard deviation 1. Find the following. a) P (z>0.5) b) P(z 1.5) c) P (-0.49 < z1.5) Question 4: If you have a normal distribution with mean 14 and standard deviation of 2. What is P(x >16)? Question 5 Professor Hardy assumes the exam scores are normally distributed and wants to grade "on a curve." The mean score was 68, with a standard deviation of 9, If he wants...
Standard Normal distribution.
With regards to a standard normal distribution complete the following: (a) Find P(Z > 0), the proportion of the standard normal distribution above the z-score of 0. (b) Find P(Z <-0.75), the proportion of the standard normal distribution below the Z-score of -0.75 (c) Find P(-1.15<z <2.04). (d) Find P(Z > -1.25). (e) Find the Z-score corresponding to Pso, the 90th percentile value.
6. Properties of the normal curve Aa Aa The following figure shows the normal distribution with the proportion of the area under the normal curve contained within one, two, and three standard deviations of the mean. The last proportion on each side, 0.13%, depicts the remaining area under the curve. Specifically, 0.13% of the area under the standard normal distribution is located above z-score values greater than the mean (H) plus three standard deviations (+30). Also, because the normal distribution...
(3.37) NOTE: The numerical values in this problem have been modified for testing purposes In its Fuel Economy Guide for 2014 model vehicles, the Environmental Protection Agency gives data on 1160 vehicles, There are a number of high outliers, mainly hybrid gas-electric vehicles. If we ignore the vehicles identified as outliers, however, the combined city and highway gas mileage of the other 1134 vehicles is approximately Normal with mean 22.8 miles per gallon (mpg) and standard deviation 5.2 mpg. The...
all questions. Do not round
answers
1. IQ scores are normally distributed with a mean of 100 and a standard deviation of 15. a. What percentage of scores is between 55 and i 15? b. In a group of 20,000 randomly selected individuals, how many have an IQ score of 130 or more? 2. A Honda Civic has its gas mileage (in miles per gallon, or mpg) normally distributed, with a mean of 33 mpg and a standard deviation of...
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