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mathematics
elementary statistics picturing

Questions and Answers of Elementary Statistics Picturing

With n = 15 and p = 0.4, find P (fewer than 3).Do the following: (a) Find the indicated binomial probability by using Table A-1 in Appendix A. (b) If np ≥ 5 and nq ≥ 5, also estimate the
Repeat Exercise 13 using variances instead of means.The ages (years) of the four U.S. presidents when they were assassinated in office are 56 (Lincoln), 49 (Garfield), 58 (McKinley), and 46
When women were allowed to become pilots of fighter jets, engineers needed to redesign the ejection seats because they had been originally designed for men only. The ACES-II ejection seats were
Using the heights of women and the cholesterol levels of women, as listed in Data Set 1 in Appendix B, analyze each of the two data sets and determine whether each appears to come from a normally
Between - 4.50Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a
Refer to Data Set 1 in Appendix B and use the systolic blood pressure levels for males.a. Using the systolic blood pressure levels for males, find the mean and standard deviation, and verify that the
Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find
Refer to Data Set 10 in Appendix B and use the durations (hours) of the NASA shuttle flights.a. Find the mean and standard deviation, and verify that the data have a distribution that is roughly
The distribution of IQ scores is a nonstandard normal distribution with a mean of 100 and a standard deviation of 15. What are the values of the mean and standard deviation after all IQ scores have
Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a sketch, and find
Heights of women are normally distributed.a. If heights of individual women are expressed in units of centimeters, what are the units used for the z scores that correspond to individual heights?b. If
You want to estimate the proportion of all U.S. college students who have the profound wisdom to take a statistics course. You obtain a simple random sample of students at New York University. Is the
There are many situations in which a normal distribution can be used as a good approximation to a random variable that has only discrete values. In such cases, we can use this continuity correction:
What does it mean when we say that the sample mean is an unbiased estimator, or that the sample mean “targets” the population mean?
Data Set 24 in Appendix B includes a sample of FICO credit rating scores from randomly selected consumers. If we investigate this sample by constructing a histogram and finding the sample mean and
In your own words describe a sampling distribution.
A statistics professor gives a test and finds that the scores are normally distributed with a mean of 25 and a standard deviation of 5. She plans to curve the scores.a. If she curves by adding 50 to
Scores on the SAT test are normally distributed with a mean of 1518 and a standard deviation of 325. Scores on the ACT test are normally distributed with a mean of 21.1 and a standard deviation of
Find the indicated value.z0.10
The distribution of IQ scores is a nonstandard normal distribution with a mean of 100 and a standard deviation of 15, and a bell-shaped graph is drawn to represent this distribution.a. What is the
Find the indicated value.z0.02
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°. Find the indicated probability, where z is the reading in degrees.P(-1.96
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°. Find the indicated probability, where z is the reading in degrees.P(z
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°. Find the indicated probability, where z is the reading in degrees.P (z
Assume that the readings on the thermometers are normally distributed with a mean of 0°C and a standard deviation of 1.00°. Find the indicated probability, where z is the reading in degrees.P(z
Find P95, the 95th percentile. This is the temperature reading separating the bottom 95% from the top 5%.
Find P1, the 1st percentile. This is the temperature reading separating the bottom 1% from the top 99%.
If 0.5% of the thermometers are rejected because they have readings that are too low and another 0.5% are rejected because they have readings that are too high, find the two readings that are cutoff
For a standard normal distribution, find the percentage of data that area. within 2 standard deviations of the mean.b. more than 1 standard deviation away from the mean.c. more than 1.96 standard
If a continuous uniform distribution has parameters of μ = 0 and σ = 1, then the minimum is - √3 and the maximum is √3a. For this distribution, find P(-1 < x < 1).b. Find P(-1 < x <
Assume that z scores are normally distributed with a mean of 0 and a standard deviation of 1.a. If P(z < a) = 0.9599, find a.b. If P(z > b) = 0.9772, find b.c. If P(z > c) = 0.0668, find
In a continuous uniform distribution, Find the mean and standard deviation for the uniform distribution represented in Figure 6-2. minimum + maximum range and o = 2 V12
Find the indicated value.z0.01
Find the indicated value.z0.05
Less than 0Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a
Greater than 0Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw a
Between - 2.50 and 5.00Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case,
Between 0.50 and 1.00Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case,
Assume that you have a data set consisting of the ages of all New York City police officers. Examination of a histogram and normal quantile plot are two different ways to assess the normality of that
If you select a simple random sample of M&M plain candies and construct a normal quantile plot of their weights, what pattern would you expect in the graph?
Identify two different characteristics of a normal quantile plot, where each characteristic would lead to the conclusion that the data are not from a normally distributed population.
What is the purpose of constructing a normal quantile plot?
This section included the statement that almost all practical applications of the binomial probability distribution can now be handled well with computer software or a TI-83/84 Plus calculator. Using
An American Airlines Boeing 767-300 aircraft has 213 seats. When fully loaded with passengers, baggage, cargo, and fuel, the pilot must verify that the gross weight is below the maximum allowable
Polygraph experiments conducted by researchers Charles R. Honts (Boise State University) and Gordon H. Barland (Department of Defense Polygraph Institute) showed that among 57 polygraph indications
The probability of flu symptoms for a person not receiving any treatment is 0.019. In a clinical trial of Lipitor (atorvastatin), a drug commonly used to lower cholesterol, 863 patients were given a
Six percent of typical people have blood that is group O and type Rh-. These people are considered to be universal donors, because they can give blood to anyone. Providence Memorial Hospital is
The U.S. Marine Corps requires that men have heights between 64 in. and 80 in.a. Find the percentage of men who meet the height requirements. Are many men denied the opportunity to become a Marine
Between 1.00 and 3.00Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case,
With the procedure called acceptance sampling, a sample of items is randomly selected and the entire batch is either rejected or accepted, depending on the results. The Telektronics Company has just
A common design requirement is that an item (such as an aircraft or theater seat) must fit the range of people who fall between the 5th percentile for women and the 95th percentile for men. If this
Birth weights in Norway are normally distributed with a mean of 3570 g and a standard deviation of 500 g.a. If the Ulleval University Hospital in Oslo requires special treatment for newborn babies
Between - 2.87 and 1.34Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case,
Between -1.20 and 1.95Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case,
Between - 3.00 andAssume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each case, draw
According to Mars (the candy company, not the planet), 24% of M&M plain candies are blue. Data Set 18 in Appendix B shows that among 100 M&Ms chosen, 27 are blue. Assuming that the claimed
Between - 1.00 and - 0.50Assume that thermometer readings are normally distributed with a mean of 0°C and a standard deviation of 1.00°C. A thermometer is randomly selected and tested. In each
When working for the Brooklyn District Attorney, investigator Robert Burton analyzed the leading digits of amounts on checks from companies that were suspected of fraud. Among 784 checks, 479 had
Based on recent results, the probability of someone in the United States being injured while using sports or recreation equipment is 1/500 (based on data from Statistical Abstract of the United
Listed below are samples of weights (ounces) of steaks listed on a restaurant menu as ?20-ounce Porterhouse? steaks (based on data collected by a student of the author). The weights are supposed to
Researchers conducted a study of helmet use and head injuries among skiers and snowboarders. Results of the study included a “P-Value” (probability value) of 0.004 (based on data from “Helmet
What is the basic difference between a situation requiring application of the permutations rule and one that requires the combinations rule?
When two dice are rolled, the total is between 2 and 12 inclusive. A student simulates the rolling of two dice by randomly generating numbers between 2 and 12. Does this simulation behave in a way
When data are summarized in a frequency distribution, the median can be found by first identifying the median class (the class that contains the median). We then assume that the values in that class
The geometric mean is often used in business and economics for finding average rates of change, average rates of growth, or average ratios. Given n values (all of which are positive), the geometric
For a given data set, there are nine deciles, denoted by D1, D2, ???, D9, which separate the sorted data into 10 groups, with about 10% of the values in each group. There are also four quintiles,
Let a population consist of the values of 1, 3, and 14. (These are the same values used in Example 1, and they are the numbers of military intelligence satellites owned by India, Japan, and Russia.)
The harmonic mean is often used as a measure of center for data sets consisting of rates of change, such as speeds. It is found by dividing the number of values n by the sum of the reciprocals of all
Use the gross amounts from movies from Data Set 9 in Appendix B. Construct a modified boxplot. Identify any outliers as defined in Part 2 of this section. Data Set 9: Movies STATDISK: Data set name
The author’s Generac generator produces voltage amounts with a mean of 125.0 volts and a standard deviation of 0.3 volt. Using Chebyshev’s theorem, what do we know about the percentage of voltage
As of this writing, there have been 42 different presidents of the United States, and four of them are alive. Listed below are the numbers of years that they lived after their first inauguration, and
Use the 40 upper leg lengths (cm) listed for females from Data Set 1 in Appendix B. Construct a modified boxplot. Identify any outliers as defined in Part 2 of this section. Data Set 1: Health Exam
Heights of women have a bell-shaped distribution with a mean of 161 cm and a standard deviation of 7 cm. Using Chebyshev’s theorem, what do we know about the percentage of women with heights that
A secondary standard mass is periodically measured and compared to the standard for one kilogram (or 1000 grams). Listed below is a sample of measured masses (in micrograms) that the secondary
Use the same scale to construct boxplots for the home voltage amounts and the generator voltage amounts from Data Set 13 in Appendix B. Use the boxplots to compare the two data sets. Data Set 13:
The author’s Generac generator produces voltage amounts with a mean of 125.0 volts and a standard deviation of 0.3 volt, and the voltages have a bell-shaped distribution. Using the empirical rule,
A student of the author earned grades of 92, 83, 77, 84, and 82 on her five regular tests. She earned grades of 88 on the final exam and 95 on her class projects. Her combined homework grade was 77.
Use the same scale to construct boxplots for the weights of the pre-1964 silver quarters and the post-1964 quarters from Data Set 20 in Appendix B. Use the boxplots to compare the two data sets.
Heights of women have a bell-shaped distribution with a mean of 161 cm and a standard deviation of 7 cm. Using the empirical rule, what is the approximate percentage of women betweena. 154 cm and 168
A student of the author earned grades of B, C, B, A, and D. Those courses had these corresponding numbers of credit hours: 3, 3, 4, 4, and 1. The grading system assigns quality points to letter
Use the same scale to construct boxplots for the weights of regular Coke and regular Pepsi from Data Set 17 in Appendix B. Use the boxplots to compare the two data sets. Data Set 17: Weights and
Find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as
Use the same scale to construct boxplots for the weights of regular Coke and diet Coke from Data Set 17 in Appendix B. Use the boxplots to compare the two data sets. Data Set 17: Weights and Volumes
As of this writing, all of the ages of winners of the Miss America Pageant are between 18 years and 24 years. Estimate the standard deviation of those ages.
The given frequency distribution describes the speeds of drivers ticketed by the Town of Poughkeepsie police. These drivers were traveling through a 30mi/h speed zone on Creek Road, which passes the
Find the standard deviation of sample data summarized in a frequency distribution table by using the formula below, where x represents the class midpoint, f represents the class frequency, and n
Find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as
A simple random sample of FICO credit rating scores was obtained, and the sorted scores are listed below. Construct a boxplot and include the values of the 5-number summary.664 693 698 714 751 753
Find the standard deviation of sample data summarized in a frequency distribution table by using the formula below, where x represents the class midpoint, f represents the class frequency, and n
Find the mean of the data summarized in the given frequency distribution. Also, compare the computed means to the actual means obtained by using the original list of data values, which are as
Refer to Data Set 9 in Appendix B and consider the gross amounts from two different categories of movies: those with R ratings, and those with ratings of PG or PG-13. Use the coefficients of
Refer to Data Set 9 in Appendix B and consider the gross amounts from two different categories of movies: Movies with R ratings and movies with ratings of PG or PG-13. Do the results appear to
Refer to Data Set 13 in Appendix B. Compare the variation from the three different sets of measured voltage levels. Refer to the indicated data set in Appendix B. Use computer software or a
Listed below are amounts of strontium-90 (in millibecquerels or mBq) in a simple random sample of baby teeth obtained from Pennsylvania residents born after 1979 (based on data from ?An Unexpected
Use the same list of 24 sorted values given for Exercises 15-18. Find the indicated percentile or quartile.P20
Use the given sorted values, which are the numbers of points scored in the Super Bowl for a recent period of 24 years. Find the percentile corresponding to the given number of points.36 37 37 39 39
Use the given sorted values, which are the numbers of points scored in the Super Bowl for a recent period of 24 years. Find the percentile corresponding to the given number of points.36 37 37 39 39
Listed below are the playing times (in seconds) of songs that were popular at the time of this writing. (The songs are by Timberlake, Furtado, Daughtry, Stefani, Fergie, Akon, Ludacris, Beyonce,
Philip Seymour Hoffman was 38 years of age when he won a Best Actor Oscar for his role in Capote. The Oscar-winning Best Actors have a mean age of 43.8 years and a standard deviation of 8.9 years.a.
When designing a new thrill ride for an amusement park, the designer must consider the sitting heights of males. Listed below are the sitting heights (in millimeters) obtained from a simple random

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