Deck 7: Continuous Probability Distributions

Question 1

The total area within any continuous probability distribution is equal to 1.00.

Answer 1

True

Question 2

The uniform probability distribution's standard deviation is proportional to the distribution's range.

Answer 2

True

Question 3

Some normal probability distributions are positively skewed.

Answer 3

False

Question 4

For a normal probability distribution,about 95 percent of the area under normal curve is within plus and minus two standard deviations of the mean and practically all (99.73 percent)of the area under the normal curve is within three standard deviations of the mean.

Question 5

The Empirical Rule of probability can be applied to the uniform probability distribution.

Question 6

The uniform probability distribution is symmetric about the mean and median.

Question 7

For any continuous probability distribution,the probability,P(x),of any value of the random variable,X,can be computed.

Question 8

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

Question 9

In a uniform probability distribution,P(x)is constant between the distribution's minimum and maximum values.

Question 10

Some normal probability distributions have different arithmetic means and different standard deviations.

Question 11

Areas within a continuous probability distribution represent probabilities.

Question 12

Some normal probability distributions have equal arithmetic means,but their standard deviations may be different.

Question 13

The total area under the normal curve is 100%.

Question 14

For a uniform probability distribution,the probability of any event is equal to 1/(b-a).

Question 15

The uniform probability distribution is symmetric about the mode.

Question 16

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

Question 17

The area under the normal curve within plus and minus one standard deviation of the mean is about 68.26%.

Question 18

Asymptotic means that the normal curve gets closer and closer to the X-axis but never actually touches it.

Question 19

The uniform probability distribution's shape is a rectangle.

Question 20

The total area within a continuous probability distribution is equal to 100.

Question 21

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

Question 22

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

Question 23

Which of the following is NOT true regarding the normal distribution?

A)Mean,median and mode are all equal
B)It has a single peak
C)It is symmetrical
D)The points of the curve meet the X-axis at z = -3 and z = 3

Question 24

The mean of a normal distribution is represented by $\sigma$ .

Question 25

The shape of any uniform probability distribution is

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

Question 26

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

Question 27

The number of different normal distributions is unlimited.

Question 28

The z-scores for X values less than the mean are positive.

Question 29

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 30

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 31

The mean of any uniform probability distribution is

A)(b - a)/2
B)(a + b)/2
C)
D)n $\pi$

Question 32

The mean (µ)divides the normal curve into two identical halves.

Question 33

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 34

The standard deviation of any uniform probability distribution is

A)(b - a)/2
B)n(1 - $\pi$ )
C)
D)

Question 35

For the normal distribution,the mean plus and minus 1.96 standard deviations will include about what percent of the observations?

A)50%
B)99.7%
C)95%
D)68%

Question 36

A z-score is the distance between a selected value (X)and the population mean (µ)divided by the population standard deviation ( $\sigma$ ).

Question 37

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 38

The formula for the z-score or z-value is (X - µ)/ $\sigma$ .

Question 39

The number of different standard normal distributions is unlimited.

Question 40

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 41

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 42

The mean of a normal distribution is 400 pounds.The standard deviation is 10 pounds.What is the area between 415 pounds and the mean of 400 pounds?

A)0.5000
B)0.1932
C)0.4332
D)0.3413

Question 43

What is the proportion of the total area under the normal curve within plus and minus two standard deviations of the mean?

A)68%
B)99.7%
C)34%
D)95%

Question 44

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 45

The mean amount spent by a family of four on food per month is $500 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 46

Which of the following is true in a normal distribution?

A)Mean equals the mode and the median
B)Mode equals the median
C)Mean divides the distribution into two equal parts
D)All of the above are correct

Question 47

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 48

Which of the following is NOT a characteristic of the normal probability distribution?

A)Positively-skewed
B)Bell-shaped
C)Symmetrical
D)Asymptotic

Question 49

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 percent 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 50

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 51

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 52

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 53

The weekly mean income of a group of executives is $1000 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 54

The mean of a normally distributed group of weekly incomes of a large group of executives is $1,000 and the standard deviation is $100.What is the z-score for an income of $1,100?

A)1.00
B)2.00
C)1.683
D)-0.90

Question 55

What is the area under the normal curve between z = 0.0 and z = 2.0?

A)1.0000
B)0.7408
C)0.1359
D)0.4772

Question 56

A new extended-life light bulb has an average service life of 750 hours,with a standard deviation of 50 hours.If the service 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)99.7%

Question 57

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 58

A random variable from an experiment where outcomes are normally distributed

A)can have any value between - $\infty$ and + $\infty$ .
B)can have only a few discrete values.
C)can have a mean of 0 and a standard deviation of 1.
D)can have no values.

Question 59

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 60

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 percent 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 61

A national manufacturer of unattached garages discovered that the distribution of the lengths of time it takes 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 30 and 34 hours to erect?

A)16.29%
B)76.71%
C)3.14%
D)34.13%

Question 62

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 percent of the tires will have to be replaced.What guaranteed mileage should the manufacturer announce?

A)44,528
B)32,960
C)49,621
D)40,922

Question 63

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 20.27 mm or more?

A)41.00%
B)12.62%
C)3.59%
D)85.00%

Question 64

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 65

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 66

The annual commissions per salesperson employed by a manufacturer of light machinery averaged $40,000 with a standard deviation of $5,000.What percent of the sales persons earn between $32,000 and $42,000?

A)60.06%
B)39.94%
C)34.13%
D)81.66%

Question 67

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 percent of the test grades.What is the dividing point between an A and a B grade?

A)80
B)85
C)90
D)95

Question 68

In a standard normal distribution,µ = ______ and $\sigma$ = ______.

Question 69

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 70

The mean amount of gasoline and services charged by Key Refining Company credit customers is $70 per month.The distribution of amounts spent 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 71

The mean of a normal probability distribution is 500 and the standard deviation is 10.About 95 percent 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 72

What type of probability distribution is the normal distribution? ______________

Question 73

A large manufacturing firm tests job applicants who recently graduated from college.The 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 6 percent of the distribution.What is the lowest score a college graduate must earn to qualify for a responsible position?

A)50
B)625
C)460
D)578

Question 74

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 75

What is a graph of a normal probability distribution called? _________

Question 76

Management is considering adopting a bonus system to increase production.One suggestion is to pay a bonus on the highest 5 percent of production based on past experience.Past records indicate that,on the average,4,000 units of a small assembly are 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 percent of production,the bonus will be paid on how many units or more?

A)6255
B)5120
C)3196
D)4099

Question 77

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 78

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 students?

A)81.48
B)90.00
C)83.72
D)78.96

Question 79

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 80

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