Quiz 7: Continuous Probability Distributions

For any uniform probability distribution,the mean and standard deviation can be computed based on the maximum and minimum values of the random variable.

For a uniformly distributed random variable,x,P(x)is constant.

For a uniformly distributed random variable,x,P(x)= 1/(b − a).

When referring to the normal probability distribution,there is not just one; there is a "family" of normal probability distributions.

A group of normal distributions can have equal arithmetic means but different standard deviations.

Some normal probability distributions are positively skewed.

Within plus and minus one standard deviation of the mean,the area under any normal curve is about 68%.

The standard normal distribution is a special normal distribution with a mean of 0 and a standard deviation of 1.

The z-scores for X values greater than the mean are negative.

Nonstop Airlines determined that the mean number of passengers per flight is 152 with a standard deviation of 10 passengers. Practically all flights have between 142 and 162 passengers.

The number of different standard normal distributions is unlimited.

The normal distribution can be used to approximate a binomial distribution when nπ is less than 5.

A "continuity correction factor" is used to compute probabilities when using the normal distribution to approximate the binomial distribution.

For the exponential distribution,the mean and standard deviation are equal.

The exponential distribution is a probability distribution for a random variable measured as a rate of an event occurring.

The shape of any uniform probability distribution is ________. A)negatively skewed B)positively skewed C)rectangular D)bell-shaped

The mean of any uniform probability distribution is ________. A)(b − a)/2 B)(a + b)/2 C)∑ D)nπ

The standard deviation of any uniform probability distribution is ________. A)(b - a)/2 B)n(1 - π) C) D) )

The upper and lower limits of a uniform probability distribution are ________. A)positive and negative infinity B)plus and minus three standard deviations C)0 and 1 D)the maximum and minimum values of the random variable

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's mean? A)120 minutes B)150 minutes C)135 minutes D)270 minutes

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the distribution's standard deviation? A)8.66 minutes B)75 minutes C)135 minutes D)270 minutes

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is less than 135 minutes? A)1.00 B)0.50 C)0.25 D)0.00

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is more than 140 minutes? A)1.00 B)0.50 C)0.333 D)0.00

The time to fly between New York City and Chicago is uniformly distributed with a minimum of 120 minutes and a maximum of 150 minutes. What is the probability that a flight is between 125 and 140 minutes? A)1.00 B)0.50 C)0.33 D)10.00

What is an important similarity between the uniform and normal probability distributions? A)The mean,median,and mode are all equal. B)The mean and median are equal. C)They are negatively skewed. D)About 68% of all observations are within one standard deviation of the mean.

Which of the following is true regarding the normal distribution? A)The mean,median,and mode are all equal. B)It has two modes. C)It is asymmetrical. D)The points of the curve meet the x-axis at z = −3 and z = 3.

For the normal distribution,the mean plus and minus two standard deviations will include about what percent of the observations? A)50% B)99.7% C)95% D)68%

For a standard normal distribution,what is the probability that z is greater than 1.75? A)0.0401 B)0.0459 C)0.4599 D)0.9599

What is the area under the normal curve between z = 0.0 and z = 1.79? A)0.4633 B)0.0367 C)0.9599 D)0.0401

What is the area under the normal curve between z = −1.0 and z = −2.0? A)0.0228 B)0.3413 C)0.1359 D)0.4772

What is the probability that z is between 0.0 and 2.0? A)1.0000 B)0.7408 C)0.1359 D)0.4772

The mean amount spent by a family of four on food is $500 per month with a standard deviation of $75. Assuming that the food costs are normally distributed,what is the probability that a family spends less than $410 per month? A)0.2158 B)0.8750 C)0.0362 D)0.1151

Which of the following is a characteristic of the normal probability distribution? A)It's positively skewed. B)It's bell-shaped. C)It's asymmetrical. D)It's rectangular.

For a normal distribution,what is the likelihood (expressed as a percentage)that a random variable is within plus and minus two standard deviations of the mean? A)68.26% B)99.74% C)34.13% D)95.44%

The mean score of a college entrance test is 500; the standard deviation is 75. The scores are normally distributed. What percent of the students scored below 320? A)About 50.82% B)About 34.13% C)About 7.86% D)About 0.82%

The weekly incomes of a large group of executives are normally distributed with a mean of $2,000 and a standard deviation of $100. What is the z-score for an income of $2,100? A)1.00 B)2.00 C)1.683 D)−0.90

A new extended-life light bulb has an average life of 750 hours,with a standard deviation of 50 hours. If the life of these light bulbs approximates a normal distribution,about what percent of the distribution will be between 600 hours and 900 hours? A)95% B)68% C)34% D)99.74%

A study of a company's practice regarding the payment of invoices revealed that an invoice was paid an average of 20 days after it was received. The standard deviation equaled five days. Assuming that the distribution is normal,what percent of the invoices were paid within 15 days of receipt? A)15.87% B)37.91% C)34.13% D)86.74%

An accelerated life test on a large number of type-D alkaline batteries revealed that the mean life for a particular use before they failed is 19.0 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.2 hours. About 95.44% of the batteries failed between what two values? A)8.9 and 18.9 B)12.2 and 14.2 C)14.1 and 22.1 D)16.6 and 21.4

The mean of a normal distribution is 400 pounds. The standard deviation is 10 pounds. What is the probability of a weight between 415 pounds and the mean of 400 pounds? A)0.5000 B)0.1932 C)0.4332 D)0.3413

The distribution of the annual incomes of a group of middle management employees approximated a normal distribution with a mean of $37,200 and a standard deviation of $800. About 68% of the incomes lie between what two incomes? A)$30,000 and $40,000 B)$36,400 and $38,000 C)$34,800 and $39,600 D)$35,600 and $38,800

Which of the following is true in a normal distribution? A)The mean equals zero. B)The mode and the third quartile are equal. C)The mean divides the distribution into two equal areas. D)The area under the curve is 0.68.

Tables of normal distribution probabilities are found in many statistics books. These probabilities are calculated from a normal distribution with ________. A)a mean of 1 and a standard deviation of 1 B)a mean of 100 and a standard deviation of 15 C)a mean of 0 and a standard deviation of 15 D)a mean of 0 and a standard deviation of 1

Two normal distributions are compared. One has a mean of 10 and a standard deviation of 10. The second normal distribution has a mean of 10 and a standard deviation of 2. Which of the following is true? A)The locations of the distributions are different. B)The distributions are from two different families of distributions. C)The dispersions of the distributions are different. D)The dispersions of the distributions are the same.

A normally distributed random variable has ________. A)any value between −∞ and + ∞ B)discrete values C)any value between specified minimum and maximum values D)only two values,success and failure

The total area of a normal probability distribution is ________. A)between −3.0 and 3.0 B)1.00 C)dependent on a value of z D)approximated by the binomial distribution

In an illustration of a normal probability distribution,a shaded area represents ________. A)a permutation B)a combination C)a probability D)a standard deviation

The standard normal probability distribution is unique because it has ________. A)a mean of 1 and any standard deviation B)any mean and a standard deviation of 1 C)a mean of 0 and any standard deviation D)a mean of 0 and a standard deviation of 1

The weekly mean income of a group of executives is $1,000 and the standard deviation of this group is $100. The distribution is normal. What percent of the executives have an income of $925 or less? A)About 15% B)About 85% C)About 50% D)About 23%

The weight of cans of fruit is normally distributed with a mean of 1,000 grams and a standard deviation of 50 grams. What percent of the cans weigh 860 grams or less? A)0.0100 B)0.8400 C)0.0026 D)0.0001

What is a normal distribution with a mean of 0 and a standard deviation of 1 called? A)Frequency distribution B)Z-score C)Standard normal distribution D)Binomial probability distribution

The seasonal output of a new experimental strain of pepper plants was carefully weighed. The mean weight per plant is 15.0 pounds,and the standard deviation of the normally distributed weights is 1.75 pounds. Of the 200 plants in the experiment,how many produced peppers weighing between 13 and 16 pounds? A)100 B)118 C)197 D)53

Ball-Bearings,Inc. produces ball bearings automatically on a Kronar BBX machine. For one of the ball bearings,the mean diameter is set at 20.00 mm (millimeters). The standard deviation of the production over a long period of time was computed to be 0.150 mm. What percent of the ball bearings will have diameters of 20.27 mm or more? A)41.00% B)12.62% C)3.59% D)85.00%

A national manufacturer of unattached garages discovered that the distribution of the time for two construction workers to erect the Red Barn model is normally distributed with a mean of 32 hours and a standard deviation of 2 hours. What percent of the garages take between 32 and 34 hours to erect? A)16.29% B)76.71% C)3.14% D)34.13%

A large manufacturing firm tests job applicants. Test scores are normally distributed with a mean of 500 and a standard deviation of 50. Management is considering placing a new hire in an upper-level management position if the person scores in the upper sixth percent of the distribution. What is the lowest score a new hire must earn to qualify for a responsible position? A)50 B)625 C)460 D)578

An analysis of the grades on the first test in History 101 revealed that they approximate a normal curve with a mean of 75 and a standard deviation of 8. The instructor wants to award the grade of A to the upper 10% of the test grades. To the nearest percent,what is the dividing point between an A and a B grade? A)80 B)85 C)90 D)95

The annual commissions per salesperson employed by a retailer of mobile communication devices averaged $40,000,with a standard deviation of $5,000. What percent of the salespersons earn between $32,000 and $42,000? A)60.06% B)39.94% C)34.13% D)81.66%

The mean of a normal probability distribution is 500 and the standard deviation is 10. About 95% of the observations lie between what two values? A)475 and 525 B)480 and 520 C)400 and 600 D)350 and 650

A cola-dispensing machine is set to dispense a mean of 2.02 liters into a container labeled 2 liters. Actual quantities dispensed vary,and the amounts are normally distributed with a standard deviation of 0.015 liters. What is the probability a container will have less than 2 liters? A)0.0918 B)0.3413 C)0.1926 D)0.8741

The employees of Cartwright Manufacturing are awarded efficiency ratings. The distribution of the ratings approximates a normal distribution. The mean is 400,the standard deviation is 50. What is the area under the normal curve between 400 and 482? A)0.5000 B)0.4495 C)0.3413 D)0.4750

Suppose a tire manufacturer wants to set a mileage guarantee on its new XB 70 tire. Tests revealed that the tire's mileage is normally distributed with a mean of 47,900 miles and a standard deviation of 2,050 miles. The manufacturer wants to set the guaranteed mileage so that no more than 5% of the tires will have to be replaced. What guaranteed mileage should the manufacturer announce? A)44,518 B)32,960 C)49,621 D)40,922

Customers of the Key Refining Company charge an average of $70 per month. The distribution of amounts charged is approximately normal,with a standard deviation of $10. What is the probability of selecting a credit card customer at random and finding the customer charged between $70 and $83? A)0.1962 B)0.4032 C)0.3413 D)0.4750

Management is considering a bonus system to increase production. One suggestion is to pay a bonus on the highest 5% of production based on past experience. Past records indicate that an average of 4,000 units of a small assembly is produced during a week. The distribution of the weekly production is approximately normally distributed with a standard deviation of 60 units. If the bonus is paid on the upper 5% of production,the bonus will be paid on how many units or more? A)6,255 B)5,120 C)3,196 D)4,099

The average score of 100 students taking a statistics final was 70,with a standard deviation of 7. Assuming a normal distribution,what is the probability that a student scored 90 or higher? A)0.4979 B)0.0021 C)0.9979 D)2.86

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution,what is the probability that a student scored greater than 65? A)0.2611 B)0.2389 C)0.7611 D)−0.714

The average score of 100 students taking a statistics final was 70,with a standard deviation of 7. Assuming a normal distribution,what test score separates the top 5% of the students from the lower 95% of the students? A)81.55 B)90.00 C)83.72 D)78.96

The average score of 100 students taking a statistics final was 70 with a standard deviation of 7. Assuming a normal distribution,what test score separates the top 25% of the students from the lower 75% of students? A)70.00 B)74.69 C)65.31 D)75.25

A binomial distribution has 100 trials (n = 100)with a probability of success of 0.25 (π = 0.25). To apply the normal distribution to approximate the binomial,what are the mean and standard deviation? A)µ= 100 and σ = 0.25 B)µ = 25 and σ = 100 C)µ = 25 and σ = 4.33 D)µ= 100 and σ = 2500

A binomial distribution has 50 trials (n = 50)with a probability of success of 0.50 (π = 0.50). To use the normal distribution to approximate the binomial,what are the mean and standard deviation? A)µ = 25 and σ = 3.5355 B)µ = 25 and σ = 12.5 C)µ = 25 and σ = 4.33 D)µ = 50 and σ = 100

A binomial distribution has 100 trials (n = 100)with a probability of success of 0.25 (π = 0.25). We would like to find the probability of 75 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor,what value would be used to calculate a z-score? A)74.5 B)75 C)75.5 D)25

A binomial distribution has 100 trials (n = 100)with a probability of success of 0.25 (π = 0.25). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor,what z-score should be used? A)2.079 B)2.194 C)1.963 D)0.25

A binomial distribution has 50 trials (n = 50)with a probability of success of 0.50 (π = 0.50). We would like to find the probability of 34 or more successes using the normal distribution to approximate the binomial. Applying the continuity correction factor,what z-score should be used? A)2.404 B)2.546 C)2.687 D)0.50

If an average of 12 customers are served per hour,then one customer arrives every ________. A)12 minutes B)60 minutes C)5 minutes D)10 minutes

If an average of 60 customers are served per hour,then one customer arrives every ________. A)1 minute B)60 minutes C)12 minutes D)10 minutes

If an average of 12 12 customers are served per hour,what is the probability that the next customer will arrive in 6 minutes or less? A)0.61 B)0.30 C)0.70 D)0.39

If an average of 12 customers are served per hour,what is the probability that the next customer will arrive in 3 minutes or less? A)0.55 B)0.30 C)0.45 D)0.39

The center of a normal probability distribution is ________. A)the same as the standard deviation or the distribution B)never negative C)the mean of the distribution D)always equal to zero

The z-value for a standard normal distribution ________. A)is always positive B)is always equal to zero C)can be either positive or negative D)is always equal to the value of the population mean

Consider a continuous random variable x,which is uniformly distributed between 65 and 85. The probability of x taking on a value between 75 to 90 is ________. A)0.75 B)1.00 C)0.50 D)0.075

Consider a standard normal random variable z. What is the value of z if the area to the right of z is 0.2643? A)0.72 B)0.28 C)1.46 D)0.63

The average starting salary of individuals with a master's degree in statistics is normally distributed with a mean of $48,000 and a standard deviation of $6,000. What is the probability that a randomly selected individual with a master's in statistics will get a starting salary of at least $55,000? A)0.121 B)0.891 C)0.379 D)0.098

A college professor noted that the grades of his students in an introductory statistics class were normally distributed with a mean of 76.5 and a standard deviation of 9. If 67.36% of his students received grades of C or above,what is the minimum score of those students receiving a grade of at least a C? A)67.36 B)72.45 C)66.56 D)70.00