Deck 7: Continuous Probability Distributions

Question 1

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

Answer 1

True

Question 2

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

Answer 2

0.50

Question 3

The mean of any uniform probability distribution is _________.

A)(b - a)/2
B)(a + b)/2
C)
D)nπ

Answer 3

(a + b)/2

Question 4

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

Question 5

The standard deviation of any uniform probability distribution is ____________.

A)(b - a)/2
B)n(1 - π)
C)
D)

Question 6

The number of different standard normal distributions is unlimited.

Question 7

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

Question 8

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

Question 9

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

Question 10

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

Question 11

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

Question 12

The shape of any uniform probability distribution is ____________.

A)Negatively skewed
B)Positively skewed
C)Rectangular
D)Bell-shaped

Question 13

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

Question 14

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

Question 15

Some normal probability distributions are positively skewed.

Question 16

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

Question 17

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

Question 18

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

Question 19

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)0.5
C)0.333
D)0.00

Question 20

Non-stop 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.

Question 21

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%

Question 22

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

Question 23

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%

Question 24

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

Question 25

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

Question 26

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.

Question 27

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

Question 28

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)99.47%

Question 29

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.

Question 30

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%

Question 31

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.

Question 32

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

Question 33

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

Question 34

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

Question 35

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%

Question 36

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.

Question 37

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.

Question 38

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

Question 39

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

Question 40

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

Question 41

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

Question 42

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

Question 43

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

Question 44

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

Question 45

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)6255
B)5120
C)3196
D)4099

Question 46

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

Question 47

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.

Question 48

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

Question 49

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%

Question 50

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%

Question 51

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 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

Question 52

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

Question 53

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

Question 54

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

Question 55

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%

Question 56

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%

Question 57

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

Question 58

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

Question 59

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

Question 60

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

Question 61

The expected value of a uniform distribution is computed using the formula _________.

Question 62

The proportion of the area under a normal curve that is to the right of z = -1.71 is _______.

Question 63

In a standard normal distribution, µ = ______ and σ = _____.

Question 64

The mean of a normal probability distribution is 60 and the standard deviation is 5. The percent of observations that are between 50 and 70 is ______.

Question 65

The proportion of the area under a normal curve that is to the right of z = -1.21 is _______.

Question 66

In a uniform distribution, with a minimum, a, and maximum, b, the probability that the random variable, x, is between a and b is ___________.

Question 67

The proportion of the area under a normal curve that is to the right of a z score, and that is equal to zero, is ________.

Question 68

In a uniform distribution, with a minimum, a, and maximum, b, the probability that the random variable, x, is between a and (b - a)/2 is ___________.

Question 69

The proportion of the area under a normal curve that is to the left of z = 1.40 is _______.

Question 70

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

Question 71

The weight of a bag of corn chips is normally distributed with a mean of 22 ounces and a standard deviation of 0.5 ounces. The probability that a bag of corn chips weighs more than 23 ounces is ____.

Question 72

In a graph of the uniform distribution, probabilities are represented by ___________.

Question 73

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

Question 74

The shape of the uniform distribution is ___________.

Question 75

A sample of 500 part-time students revealed that their annual incomes were normally distributed with a mean income of $30,000 and a standard deviation of $3,000. The number of students that earned between $27,000 and $33,000 is _____.

Question 76

A z-value measures the distance between an outcome, x, and its population mean in terms of the number of _____________________.

Question 77

For normally distributed random variables, the _________ makes probability statements based on specific values of the standard deviation.

Question 78

About ______% of the area under the normal curve is within plus two and minus two standard deviations of the mean.

Question 79

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

Question 80

The proportion of the area under a normal curve that is to the left of z = 0.50 is _______.