Introductory Statistics
1st Edition
ISBN: 9781938168208
Author: Barbara Illowsky, Susan Dean
Publisher: OpenStax College
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Textbook Question
Chapter 6, Problem 23P
Suppose X ~N( 12, 6). What is the z-score of x = 2?
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In order to find probability, you can use this formula in Microsoft Excel:
The best way to understand and solve these problems is by first drawing a bell curve and marking key points such as x, the mean, and the areas of interest. Once marked on the bell curve, figure out what calculations are needed to find the area of interest.
=NORM.DIST(x, Mean, Standard Dev., TRUE).
When the question mentions “greater than” you may have to subtract your answer from 1.
When the question mentions “between (two values)”, you need to do separate calculation for both values and then subtract their results to get the answer.
1.
Compute the probability of a value between 44.0 and 55.0.
(The question requires finding probability value between 44 and 55. Solve it in 3 steps.
In the first step, use the above formula and x = 44, calculate probability value.
In the second step repeat the first step with the only difference that x=55.
In the third step, subtract the answer of the first part from the…
If a uniform distribution is defined over the interval from 6 to 10, then answer the followings:
What is the mean of this uniform distribution?
Show that the probability of any value between 6 and 10 is equal to 1.0
Find the probability of a value more than 7.
Find the probability of a value between 7 and 9.
The closing price of Schnur Sporting Goods Inc. common stock is uniformly distributed between $20 and $30 per share. What is the probability that the stock price will be:
More than $27?
Less than or equal to $24?
The April rainfall in Flagstaff, Arizona, follows a uniform distribution between 0.5 and 3.00 inches.
What is the mean amount of rainfall for the month?
What is the probability of less than an inch of rain for the month?
What is the probability of exactly 1.00 inch of rain?
What is the probability of more than 1.50 inches of rain for the month?
The best way to solve this problem is begin by creating a chart. Clearly mark the range, identifying the lower and upper…
Problem 1:
The mean hourly pay of an American Airlines flight attendant is normally distributed with a mean of 40 per hour and a standard deviation of 3.00 per hour. What is the probability that the hourly pay of a randomly selected flight attendant is:
Between the mean and $45 per hour?
More than $45 per hour?
Less than $32 per hour?
Problem 2:
The mean of a normal probability distribution is 400 pounds. The standard deviation is 10 pounds.
What is the area between 415 pounds and the mean of 400 pounds?
What is the area between the mean and 395 pounds?
What is the probability of randomly selecting a value less than 395 pounds?
Problem 3:
In New York State, the mean salary for high school teachers in 2022 was 81,410 with a standard deviation of 9,500. Only Alaska’s mean salary was higher. Assume New York’s state salaries follow a normal distribution.
What percent of New York State high school teachers earn between 70,000 and 75,000?
What percent of New York State high school…
Chapter 6 Solutions
Introductory Statistics
Ch. 6 - What is the z-score of x, when x = 1 and...Ch. 6 - Fill In the blanks. Jerome averages 16 points a...Ch. 6 - Use the Information in Example 6.3 to answer the...Ch. 6 - In 2012, 1,664,479 students took the SAT exam. The...Ch. 6 - Suppose X has a normal distribution with mean 25...Ch. 6 - The scores on a college entrance exam have an...Ch. 6 - If the area to the left of x is 0.012, then what...Ch. 6 - The golf scores for a school team were normally...Ch. 6 - The golf scores for a school team were normally...Ch. 6 - Use the Information in Example 6.10 to answer the...
Ch. 6 - Two thousand students took an exam. The scores on...Ch. 6 - Using the information from Example 6.12, answer...Ch. 6 - A bottle of water contains 12.05 fluid ounces with...Ch. 6 - A normal distribution has a mean of 61 and a...Ch. 6 - X~N(1,2)=Ch. 6 - A company manufactures rubber balls. The mean...Ch. 6 - X~N(-4, 1) What is the median?Ch. 6 - X~N(3,5)=Ch. 6 - X~N(2,1)=Ch. 6 - What does a z-score measure?Ch. 6 - What does standardizing a normal distribution do...Ch. 6 - Is X ~N(0, 1) a standardized normal distribution?...Ch. 6 - What is the z-score of x = 12, if it is two...Ch. 6 - What is the z-score of x = 9, if it is 1.5...Ch. 6 - What is the z-score of x = —2, if it is 2.78...Ch. 6 - What is the z-score of x = 7, if it is 0.133...Ch. 6 - Suppose X~ N(2, 6). What value of x has a z-score...Ch. 6 - Suppose X~ N(8, 1). ‘What value of x has a z-score...Ch. 6 - Suppose X ~N(9, 5). What value of x has a z-score...Ch. 6 - Suppose X~ N(2, 3). That value of x has a z-score...Ch. 6 - Suppose X ~N(4, 2). What value of x is 1.5...Ch. 6 - Suppose X ~N(4, 2). What value of x is two...Ch. 6 - Suppose X ~N(8, 9). What value of x is 0.67...Ch. 6 - Suppose X ~N(—1, 2). What is the z-score of x = 2?Ch. 6 - Suppose X ~N( 12, 6). What is the z-score of x =...Ch. 6 - Suppose X ~N(9, 3). What is the z-score of x = 9?Ch. 6 - Suppose a normal distribution has a mean of six...Ch. 6 - In a normal distribution, x = 5 and z = —1.25....Ch. 6 - In a normal distribution, x = 3 and z = 0.67. This...Ch. 6 - In a normal distribution, x = —2 and z = 6. This...Ch. 6 - In a normal distribution, x = —5 and z = —3.14....Ch. 6 - In a normal distribution, x= 6 and z —1.7. This...Ch. 6 - About what percent of x values from a normal...Ch. 6 - About what percent of the x values from a normal...Ch. 6 - About what percent of x values lie between the...Ch. 6 - Suppose X N( 15, 3). Between what x values does...Ch. 6 - Suppose X~ N(—3, 1). Between what x values does...Ch. 6 - Suppose X ~N(—3, 1). Between what x values does...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - About what percent of x values lie between the...Ch. 6 - Use the following information to answer the next t...Ch. 6 - Use the following information to answer the next t...Ch. 6 - How would you represent the area to the left of...Ch. 6 - What is the area to the right of one? Figure 6.13Ch. 6 - Is P(x < 1) equal to P(x1) ? ‘by?Ch. 6 - How would you represent the area to the left of...Ch. 6 - What is the area to the right of three? Figure...Ch. 6 - If the area to the left of x in a normal...Ch. 6 - If the area to the tight of x in a normal...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - X~N(6, 2) Find the probability that x is between...Ch. 6 - X~N(—3, 4) Find the probability that x is between...Ch. 6 - X~N(4,5) Find the maxium of x in the bottom...Ch. 6 - Use the following information to answer the next...Ch. 6 - Find the probability that a CD player will last...Ch. 6 - Find the 70th percentile of the distribution for...Ch. 6 - Use the following information to answer the next r...Ch. 6 - Use the following information to answer the next r...Ch. 6 - The length of time to find it takes to find a...Ch. 6 - The heights of the 430 National Basketball...Ch. 6 - The systolic blood pressure (given In millimeters)...Ch. 6 - Kyle’s doctor told him that the z-score for his...Ch. 6 - Height and weight are two measurements used to...Ch. 6 - In 2005, 1,475,623 students heading to college...Ch. 6 - Use the following information (0 answer the next...Ch. 6 - Use the following information (0 answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - Use the following information to answer the next...Ch. 6 - According to a study done by De Anza students, the...Ch. 6 - IQ is normally distributed with a mean of 100 and...Ch. 6 - The percent of fat calories that a person In...Ch. 6 - Suppose that the distance of fly balls hit to the...Ch. 6 - In China, four-ear-olds average three bows a day...Ch. 6 - In the 1992 presidential election, Alaska's 40...Ch. 6 - Suppose that the duration of a particular type of...Ch. 6 - Tern Vogel, an amateur motorcycle racer, averages...Ch. 6 - Thuy Dau, Ngoc Bui, Sam Su, and Lan Voung...Ch. 6 - Suppose that Ricardo and Anita attend different...Ch. 6 - Table 6.4 shows a sample of the maximum capacity...Ch. 6 - An expert witness for a paternity lawsuit...Ch. 6 - A NUMMI assembly Line, which has been operating...Ch. 6 - We flip a coin 100 times (n = 100) and note that...Ch. 6 - A $1 scratch off lotto ticket will be a inner one...Ch. 6 - Facebook provides a variety of statistics on its...
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