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Questions and Answers of
Business Statistics
Suppose that a category of world-class runners are known to run a marathon (26 miles) in an average of 145 minutes with a standard deviation of 14 minutes. Consider 49 of the races. Let X̅ the
The length of songs in a collector’s iTunes album collection is uniformly distributed from two to 3.5 minutes. Suppose we randomly pick five albums from the collection. There are a total of 43
In 1940 the average size of a U.S. farm was 174 acres. Let’s say that the standard deviation was 55 acres. Suppose we randomly survey 38 farmers from 1940. a. In words, X = b. In words, X C. X N =
Determine which of the following are true and which are false. Then, in complete sentences, justify your answers.a. When the sample size is large, the mean of X̅ is approximately equal to the mean
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of about ten. Suppose that 16 individuals are randomly
The distribution of income in some Third World countries is considered wedge shaped (many very poor people, very few middle income people, and even fewer wealthy people). Suppose we pick a country
Which of the following is NOT TRUE about the distribution for averages?a. The mean, median, and mode are equal.b. The area under the curve is one.c. The curve never touches the x-axis.d. The curve is
The cost of unleaded gasoline in the Bay Area once followed an unknown distribution with a mean of $4.59 and a standard deviation of $0.10. Sixteen gas stations from the Bay Area are randomly chosen.
A large population has skewed data with a mean of 70 and a standard deviation of 6. Samples of size 100 are taken, and the distribution of the means of these samples is analyzed.a. Will the
A population has a standard deviation of 50. It is sampled with samples of size 100. What is the variance of the means of the samples?
A farmer picks pumpkins from a large field. The farmer makes samples of 260 pumpkins and inspects them. If one in fifty pumpkins are not fit to market and will be saved for seeds, what is the
A store surveys customers to see if they are satisfied with the service they received. Samples of 25 surveys are taken.One in five people are unsatisfied. What is the variance of the mean of the
A company gives an anonymous survey to its employees to see what percent of its employees are happy. The company is too large to check each response, so samples of 50 are taken, and the tendency is
A pollster asks a single question with only yes and no as answer possibilities. The poll is conducted nationwide, so samples of 100 responses are taken. There are four yes answers for each no answer
The mean of the sampling distribution of sample proportions has a value of p of 0.3, and sample size of 40.a. Is there a difference in the expected value if p and q reverse roles?b. Is there a
A school has 500 students. Usually, there are an average of 20 students who are absent. If a sample of 30 students is taken on a certain day, what is the probability that at least 2 students in the
A bottle of water contains 12.05 fluid ounces with a standard deviation of 0.01 ounces. Define the random variable X in words. X = ____________.
A normal distribution has a mean of 61 and a standard deviation of 15. What is the median?
A company manufactures rubber balls. The mean diameter of a ball is 12 cm with a standard deviation of 0.2 cm. Define the random variable X in words. X = ______________.
What is the median?X ~ N(–4, 1)
Fill in the blank X ~ N(3, 5)σ = _______
Fill in the blank X ~ N(–2, 1)μ = _______
What does a z-score measure?
What does standardizing a normal distribution do to the mean?
Is X ~ N(0, 1) a standardized normal distribution? Why or why not?
What is the z-score of x = 12, if it is two standard deviations to the right of the mean?
What is the z-score of x = 9, if it is 1.5 standard deviations to the left of the mean?
What is the z-score of x = –2, if it is 2.78 standard deviations to the right of the mean?
What is the z-score of x = 7, if it is 0.133 standard deviations to the left of the mean?
Suppose X ~ N(2, 6). What value of x has a z-score of three?
Suppose X ~ N(8, 1). What value of x has a z-score of –2.25?
Suppose X ~ N(9, 5). What value of x has a z-score of –0.5?
Suppose X ~ N(2, 3). What value of x has a z-score of –0.67?
Suppose X ~ N(4, 2). What value of x is 1.5 standard deviations to the left of the mean?
Suppose X ~ N(4, 2). What value of x is two standard deviations to the right of the mean?
Suppose X ~ N(8, 9). What value of x is 0.67 standard deviations to the left of the mean?
Suppose X ~ N(12, 6). What is the z-score of x = 2?
Suppose X ~ N(9, 3). What is the z-score of x = 9?
Suppose a normal distribution has a mean of six and a standard deviation of 1.5. What is the z-score of x = 5.5?
In a normal distribution, x = 5 and z = –1.25. This tells you that x = 5 is ____ standard deviations to the ____ (right or left) of the mean.
In a normal distribution, x = 3 and z = 0.67. This tells you that x = 3 is ____ standard deviations to the ____ (right or left) of the mean.
In a normal distribution, x = –2 and z = 6. This tells you that x = –2 is ____ standard deviations to the ____ (right or left) of the mean.
In a normal distribution, x = –5 and z = –3.14. This tells you that x = –5 is ____ standard deviations to the ____ (right or left) of the mean.
In a normal distribution, x = 6 and z = –1.7. This tells you that x = 6 is ____ standard deviations to the ____ (right or left) of the mean.
About what percent of x values from a normal distribution lie within one standard deviation (left and right) of the mean of that distribution?
About what percent of the x values from a normal distribution lie within two standard deviations (left and right) of the mean of that distribution?
About what percent of x values lie between the second and third standard deviations (both sides)?
Suppose X ~ N(15, 3). Between what x values does 68.27% of the data lie? The range of x values is centered at the mean of the distribution (i.e., 15).
Suppose X ~ N(–3, 1). Between what x values does 95.45% of the data lie? The range of x values is centered at the mean of the distribution(i.e., –3).
Suppose X ~ N(–3, 1). Between what x values does 34.14% of the data lie?
About what percent of x values lie between the mean and three standard deviations?
About what percent of x values lie between the mean and one standard deviation?
About what percent of x values lie between the first and second standard deviations from the mean (both sides)?
About what percent of x values lie betwween the first and third standard deviations(both sides)?
The life of Sunshine CD players is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of
The life of Sunshine CD players is normally distributed with mean of 4.1 years and a standard deviation of 1.3 years. A CD player is guaranteed for three years. We are interested in the length of
How would you represent the area to the left of one in a probability statement? 1 x
What is the area to the right of one? 1 X
Is P(x < 1) equal to P(x ≤ 1)? Why?
How would you represent the area to the left of three in a probability statement? 3
What is the area to the right of three? 3 X
If the area to the left of x in a normal distribution is 0.123, what is the area to the right of x?
If the area to the right of x in a normal distribution is 0.543, what is the area to the left of x?Use the following information to answer the next four exercises:X ~ N(54, 8)
Find the probability that x > 56.
Find the probability that x < 30.
X ~ N(6, 2)Find the probability that x is between three and nine.
X ~ N(–3, 4)Find the probability that x is between one and four.
X ~ N(4, 5)Find the maximum of x in the bottom quartile.
Find the probability that a CD player will break down during the guarantee period.a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.b. P(0 The life
Find the probability that a CD player will last between 2.8 and six years.a. Sketch the situation. Label and scale the axes. Shade the region corresponding to the probability.b. P(__________ The life
What is the median recovery time?a. 2.7b. 5.3c. 7.4d. 2.1 The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days and a standard deviation of
What is the z-score for a patient who takes ten days to recover?a. 1.5b. 0.2c. 2.2d. 7.3 The patient recovery time from a particular surgical procedure is normally distributed with a mean of 5.3 days
The length of time to find it takes to find a parking space at 9 A.M. follows a normal distribution with a mean of five minutes and a standard deviation of two minutes. If the mean is significantly
The heights of the 430 National Basketball Association players were listed on team rosters at the start of the 2005–2006 season. The heights of basketball players have an approximate normal
The systolic blood pressure (given in millimeters) of males has an approximately normal distribution with mean μ =125 and standard deviation σ = 14. Systolic blood pressure for males follows a
Kyle’s doctor told him that the z-score for his systolic blood pressure is 1.75. Which of the following is the best interpretation of this standardized score? The systolic blood pressure (given in
Height and weight are two measurements used to track a child’s development. TheWorld Health Organization measures child development by comparing the weights of children who are the same height and
In 2005, 1,475,623 students heading to college took the SAT. The distribution of scores in the math section of the SAT follows a normal distribution with mean μ = 520 and standard deviation σ =
What is the probability of spending more than two days in recovery?a. 0.0580b. 0.8447c. 0.0553d. 0.9420 The patient recovery time from a particular surgical procedure is normally distributed with a
Based upon the given information and numerically justified, would you be surprised if it took less than one minute to find a parking space?a. Yesb. Noc. Unable to determine The patient recovery time
Find the probability that it takes at least eight minutes to find a parking space.a. 0.0001b. 0.9270c. 0.1862d. 0.0668 The length of time it takes to find a parking space at 9 A.M. follows a normal
Seventy percent of the time, it takes more than how many minutes to find a parking space?a. 1.24b. 2.41c. 3.95d. 6.05 The length of time it takes to find a parking space at 9 A.M. follows a normal
IQ is normally distributed with a mean of 100 and a standard deviation of 15. Suppose one individual is randomly chosen. Let X = IQ of an individual.a. X ~ _____(_____,_____)b. Find the probability
The percent of fat calories that a person in America consumes each day is normally distributed with a mean of about 36 and a standard deviation of 10. Suppose that one individual is randomly chosen.
In China, four-year-olds average three hours a day unsupervised. Most of the unsupervised children live in rural areas, considered safe. Suppose that the standard deviation is 1.5 hours and the
In the 1992 presidential election, Alaska’s 40 election districts averaged 1,956.8 votes per district for President Clinton.The standard deviation was 572.3. (There are only 40 election districts
Suppose that the duration of a particular type of criminal trial is known to be normally distributed with a mean of 21 days and a standard deviation of seven days.a. In words, define the random
Terri Vogel, an amateur motorcycle racer, averages 129.71 seconds per 2.5 mile lap (in a seven-lap race) with a standard deviation of 2.28 seconds. The distribution of her race times is normally
Suppose that Ricardo and Anita attend different colleges. Ricardo’s GPA is the same as the average GPA at his school.Anita’s GPA is 0.70 standard deviations above her school average. In complete
An expert witness for a paternity lawsuit testifies that the length of a pregnancy is normally distributed with a mean of 280 days and a standard deviation of 13 days. An alleged father was out of
A NUMMI assembly line, which has been operating since 1984, has built an average of 6,000 cars and trucks a week.Generally, 10% of the cars were defective coming off the assembly line. Suppose we
We flip a coin 100 times (n = 100) and note that it only comes up heads 20% (p = 0.20) of the time. The mean and standard deviation for the number of times the coin lands on heads is μ = 20 and σ =
Which type of distribution does the graph illustrate? 0 1 2 3 4 5 6 789 10 X
Which type of distribution does the graph illustrate? 0 1 2 3 T4 4 5 X 6 7 8 9 10
Which type of distribution does the graph illustrate? X -3 -2 -1 0 1 2 3
What does the shaded area represent? P(___ X 0 1 2 3 4 56 789 10
What does the shaded area represent? P(___ X 01 2 3 4 5 6 7 8 9 10
For a continuous probablity distribution, 0 ≤ x ≤ 15. What is P(x > 15)?
What is the area under f(x) if the function is a continuous probability density function?
For a continuous probability distribution, 0 ≤ x ≤ 10. What is P(x = 7)?
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