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mathematics
business statistics

Questions and Answers of Business Statistics

Find the z value that corresponds to the given area. 0.8962
About 12.5% of restaurant bills are incorrect. If 200 bills are selected at random, find the probability that at least 22 will contain an error. Is this likely or unlikely to occur?
Between z = −1.46 and z = −1.77Find the area under the standard normal distribution curve.
The average overseas trip cost is $2708 per visitor. If we assume a normal distribution with a standard deviation of $405, what is the probability that the cost for a randomly selected trip is more
For a certain group of individuals, the average heart rate is 72 beats per minute. Assume the variable is normally distributed and the standard deviation is 3 beats per minute. If a subject is
Twenty-two percent of work injuries are back injuries. If 400 work-injured people are selected at random, find the probability that 92 or fewer have back injuries.
Between z = 1.09 and z = 1.83Find the area under the standard normal distribution curve.
According to the World Almanac, 72% of households own smartphones. If a random sample of 180 households is selected, what is the probability that more than 115 but fewer than 125 have a smartphone?
In the second quarter of 2015, the average movie ticket cost $8.61. In a random sample of 50 movie tickets from various areas, what is the probability that the mean cost exceeds $8.00, given that the
The average number of potholes per 10 miles of paved U.S. roads is 130. Assume this variable is approximately normally distributed and has a standard deviation of 5. Find the probability that a
Seventy-six percent of small business owners do not have a college degree. If a random sample of 60 small business owners is selected, find the probability that exactly 48 will not have a college
To the left of z = −1.87Find the area under the standard normal distribution curve.
The average retail price of gasoline (all types) for 2014 was 342 cents. What would the standard deviation have to be in order for there to be a 15% probability that a gallon of gas costs less than
The average number of earthquakes that occur in Los Angeles over one month is 36. (Most are undetectable.) Assume the standard deviation is 3.6. If a random sample of 35 months is selected, find the
In a recent year, the rate of U.S. home ownership was 65.9%. Choose a random sample of 120 households across the United States. What is the probability that 65 to 85 (inclusive) of them live in homes
To the right of z = 0.37Find the area under the standard normal distribution curve.
The average amount a slot machine makes per month is $8000. This is after payouts. Assume the earnings are normally distributed with a standard deviation of $750. Find the amount of earnings if 15%
The average number of moves a person makes in his or her lifetime is 12. If the standard deviation is 3.2, find the probability that the mean of a sample of 36 people isa. Less than 10b. Greater than
The average cost of repairing an smartphone is $120 with a standard deviation of $10.50. The costs are normally distributed. If 15% of the costs are considered excessive, find the cost in dollars
What formula is used to gain information about an individual data value when the variable is normally distributed?
In a recent year, about 22% of Americans 18 years and older are single. What is the probability that in a random sample of 200 Americans 18 or older more than 30 are single?
Between z = 0 and z = 1.93Find the area under the standard normal distribution curve.
The average prison sentence for a person convicted of second-degree murder is 15 years. If the sentences are normally distributed with a standard deviation of 2.1 years, find these probabilities:a. A
The average lifetime of smoke detectors that a company manufactures is 5 years, or 60 months, and the standard deviation is 8 months. Find the probability that a random sample of 30 smoke detectors
Between z = 0 and z = 1.07Find the area under the standard normal distribution curve.
What are two other names for a normal distribution?
The average salary for graduates entering the actuarial field is $63,000. If the salaries are normally distributed with a standard deviation of $5000, find the probability thata. An individual
What does the central limit theorem say about the shape of the distribution of sample means?
What percentage of the area falls below the mean? Above the mean?
What is the standard deviation of the sample means called? What is the formula for this standard deviation?
Using the standard normal distribution, find each probability.a. P(z > 1.66)b. P(z < −2.03)c. P(z > −1.19)d. P(z < 1.93)e. P(z > −1.77)
What is the total area under the standard normal distribution curve?
What is the mean of the sample means?
Using the standard normal distribution, find each probability.a. P(0 < z < 2.23)b. P(−1.75 < z < 0)c. P(−1.48 < z <1.68)d. P(1.22 < z < 1.77)e. P(−2.31 < z < 0.32)
Why is the standard normal distribution important in statistical analysis?
Why do most of the sample means differ somewhat from the population mean? What is this difference called?
Find the area under the standard normal distribution for each.a. Between z = 1.10 and z = −1.80b. To the right of z = 1.99c. To the right of z = −1.36d. To the left of z = −2.09e. To the left
If samples of a specific size are selected from a population and the means are computed, what is this distribution of means called?
Find the area under the standard normal distribution curve for each.a. Between z = 0 and z = 2.06b. Between z = 0 and z = 0.53c. Between z = 1.26 and 1.74d. Between z = −1.02 and z = 1.63e. Between
A worker in the automobile industry works an average of 43.7 hours per week. If the distribution is approximately normal with a standard deviation of 1.6 hours, what is the probability that a
Find the z value that corresponds to the given area. 0.0188
Find P(z < 2.3 or z > −1.2).
Find P(z > 2.3 and z < −1.2).
Find the equation for the standard normal distribution by substituting 0 for Î¼ and 1 for Ïƒ in the equation .-х- р?/2 «3) y: У 3 oV 2л
Find P(−1 < z < 1), P(−2 < z < 2), and P(−3 < z < 3).How do these values compare with the empirical rule?
Find the z value that corresponds to the given area. 0.9671-
Find the z value that corresponds to the given area. 0.0239
Find the z value that corresponds to the given area. 0.4175
Find the probabilities for each, using the standard normal distribution.P(−2.07 < z < 1.88)
If a distribution of raw scores were plotted and then the scores were transformed to z scores, would the shape of the distribution change? Explain your answer.
Consider the distribution of monthly Social Security (OASDI) payments. Assume a normal distribution with a standard deviation of $120. If one-fourth of the payments are above $1255.94, what is the
The mean temperature for a July in Pittsburgh is 73°. Assuming a normal distribution, what would the standard deviation have to be if 5% of the days have a temperature of at least 85°?
Find the probabilities for each, using the standard normal distribution.P(z < −1.51)
Suppose that the mathematics SAT scores for high school seniors for a specific year have a mean of 456 and a standard deviation of 100 and are approximately normally distributed. If a subgroup of
Find the probabilities for each, using the standard normal distribution.P(z > 0.82)
Find the probabilities for each, using the standard normal distribution.P(z > 2.33)
The top web browser in 2015 was Chrome with 51.74% of the market. In a random sample of 250 people, what is the probability that fewer than 110 did not use Chrome?
A report stated that the average number of times a cat returns to its food bowl during the day is 36. Assuming the variable is normally distributed with a standard deviation of 5, what is the
In a normal distribution, find μ when σ is 6 and 3.75% of the area lies to the left of 85.
Find the probabilities for each, using the standard normal distribution.P(−0.20 < z < 1.56)
U.S. internet users spend an average of 18.3 hours a week online. If 95% of users spend between 13.1 and 23.5 hours a week, what is the probability that a randomly selected user is online less than
Find the probabilities for each, using the standard normal distribution.P(z > −1.43)
Find the probabilities for each, using the standard normal distribution.P(1.56 < z < 2.13)
Find the probabilities for each, using the standard normal distribution.P(z < 1.42)
Find the probabilities for each, using the standard normal distribution.P(−1.23 < z < 0)
Find the probabilities for each, using the standard normal distribution.P(−1.38 < z < 0)
Americans drank an average of 34 gallons of bottled water per capita in 2014. If the standard deviation is 2.7 gallons and the variable is normally distributed, find the probability that a randomly
Find the probabilities for each, using the standard normal distribution.P(0 < z < 1.96)
When is the normal distribution not a good approximation for the binomial distribution?
An advertising company plans to market a product to low-income families. A study states that for a particular area, the average income per family is $24,596 and the standard deviation is $6256. If
On the Trends in International Mathematics and Science Study (TIMSS) test in a recent year, the United States scored an average of 508 (well below South Korea, 597; Singapore, 593; Hong Kong, 572;
The average age of Amtrak passenger train cars is 19.4 years. If the distribution of ages is normal and 20% of the cars are older than 22.8 years, find the standard deviation.
What information is necessary to calculate a confidence interval?
Find the probabilities for each, using the standard normal distribution.P(0 < z < 0.95)
To qualify for a medical study, an applicant must have a systolic blood pressure in the 50% of the middle range. If the systolic blood pressure is normally distributed with a mean of 120 and a
To the right of z = −0.18Find the area under the standard normal distribution curve.
Excluding motor vehicle thefts, 26% of all larceny-thefts involved items taken from motor vehicles. Local police forces are trying to help the situation with their “Put your junk in the trunk!”
Of the total U.S. population, 37% live in the South. If 200 U.S. residents are selected at random, find the probability that at least 80 live in the South.
The mean precipitation for Miami in August is 8.9 inches. Assume that the standard deviation is 1.6 inches and the variable is normally distributed.a. Find the probability that a randomly selected
To the left of z = 1.12Find the area under the standard normal distribution curve.
The National Institute of Mental Health reports that there is a 20% chance of an adult American suffering from a psychiatric disorder. Four randomly selected adult Americans are examined for
We have provided the parameter of a Poisson random variable, X. For each exercise,a. Determine the required probabilities. Round your probability answers to three decimal places.b. Find the mean and
We have provided the parameter of a Poisson random variable, X. For each exercise,a. Determine the required probabilities. Round your probability answers to three decimal places.b. Find the mean and
We have provided the parameter of a Poisson random variable, X. For each exercise,a. Determine the required probabilities. Round your probability answers to three decimal places.b. Find the mean and
Sketch the normal curve having the parametersa. μ = −1 and σ = 2.b. μ = 3 and σ = 2.c. μ = −1 and σ = 0.5.
Researchers G. Evans and E. Kantrowitz explored the health consequences for exposure to many different environmental risks in the journal article “Socioeconomic Status and Health: The Potential
The U.S. Citizenship and Immigration Services collects and reports information about naturalized persons in Statistical Yearbook. During one year, there were 463,204 persons who became naturalized
According to the document Current Population Survey, published by the U.S. Census Bureau, 31.6% of U.S. adults 25 years old or older have a high school degree as their highest educational level. If
The Office of Aviation Enforcement and Proceedings (OAEP) publishes important consumer information about airlines in Air Travel Consumer Report. For the 12 months ending June 30, 2008, 73.7% of all
As reported by a spokesperson for Southwest Airlines, the no-show rate for reservations is 16%. In other words, the probability is 0.16 that a person making a reservation will not take the flight.
As reported in an issue of Weatherwise, according to the National Oceanic and Atmospheric Administration, people at ballparks and playgrounds are in more danger of being struck by lightning than are
In the online TIME article “America’s Health Checkup,” A. Park reported that 40% of U.S. adults get no exercise. If 250 U.S. adults are selected at random, determine the probability that the
Provide two synonyms for “the distribution of all possible sample means for samples of a given size.”
Suppose that you plan to apply the one-mean z-interval procedure to obtain a 90% confidence interval for a population mean, μ. You know that σ = 12 and that you are going to use a sample of size
The paper €œAre Babies Normal?€ by T. Clemons and M. Pagano (The American Statistician, Vol. 53, No. 4, pp. 298€“302) focused on birth weights of babies. According to
If a good typist can input 70 words per minute, but a 99% confidence interval for the mean number of words input per minute by recent applicants lies entirely below 70, what can you conclude about
Key Fact 8.3 states that, for a fixed sample size, decreasing the confidence level improves the precision of the confidence interval estimate of μ and vice versa.a. Suppose that you want to increase
Explain the difference in the formulas for the standardized and studentized versions of x̅.
True or false: A critical value is considered part of the rejection region.In problem pertain to the critical-value approach to hypothesis testing.
Suppose that you want to conduct a left-tailed hypothesis test at the 5% significance level. How must the critical value be chosen?In problem pertain to the critical-value approach to hypothesis

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