Deck 6: Probability, normal Distributions, and Z Scores

Question 1

The normal distribution has all of the following characteristics,except that

A) it is symmetrical.
B) its distribution is theoretical.
C) the total area under the curve is greater than 1.0.
D) the mean, median, and mode are equal.

Answer 1

the total area under the curve is greater than 1.0.

Question 2

The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a

A) standardized score.
B) x score.
C) normalized deviation.
D) z score.

Answer 2

z score.

Question 3

The ______ converts any normal distribution with any mean and any variance to a standard normal distribution with a mean of 0 and variance of 1.

A) normal distribution
B) standard normal distribution
C) standard normal transformation
D) unit normal table

Answer 3

standard normal transformation

Question 4

A parent decides to reward her child if he eats an average of at least five bites of his vegetables at dinner during the first week.She finds that her child ate 4 ± 0.8 (M ± SD)bites per meal for the first week.Assuming these data are normally distributed,should this parent reward her child?

A) Yes, because the z score for 5 bites is greater than 0.
B) Yes, because the z score for 5 bites is less than 0.
C) No, because the z score for 5 bites is greater than 0.
D) No, because the z score for 5 bites is less than 0.

Question 5

A researcher determines that students are active about 60 ± 12 (M ± SD)min/day.Assuming these data are normally distributed,what is the z score for students being active 48 min/week?

A) 1.0
B) -1.0
C) 0
D) There is not enough information to answer this question.

Question 6

The following distribution most closely approximates a

A) normal distribution.
B) positively skewed distribution.
C) negatively skewed distribution.
D) multimodal distribution.

Question 7

The normal distribution is symmetrical,which means that

A) scores above the mean are distributed the same as scores below the mean.
B) extreme scores are possible in a normal distribution.
C) there are an infinite number of possible normal distributions.
D) this characteristic has no practical implication.

Question 8

A therapist has a goal to reduce the mean number of patient symptoms expressed for a particular disorder to two symptoms per day.Following therapy,she determines that the z score for 2 symptoms per day is 0.Assuming the data are normally distributed,did she reach her goal?

A) No, because the z score indicates 0 improvement.
B) No, because the z score is not negative (indicating a reduction in symptoms).
C) Yes; in fact, she actually reduced the mean number of symptoms to 0.
D) Yes, because a z score of 0 is the average, or mean.

Question 9

A researcher determines that students study an average of 80 ± 20 (M ± SD)min/week.Assuming these data are normally distributed,what is the z score for students studying 60 min/week?

A) 1.0
B) -1.0
C) .3413
D) .1587

Question 10

A distribution of z scores is distributed in what type of unit of measurement?

A) Binomial outcomes
B) Probabilities
C) Standard deviation units
D) Depends on the shape of the distribution

Question 11

The standard normal distribution is normally distributed with a mean of ______ and a variance of ______.

A) 0; 1
B) 1; 0
C) any value; any positive value
D) any positive value; any value

Question 12

A theoretical distribution that evenly distributes data around the mean,median,and mode is called the

A) normal distribution.
B) bell-shaped distribution.
C) Gaussian distribution.
D) all of these.

Question 13

What is the implication for the tails of a normal distribution being asymptotic?

A) that scores above the mean are distributed the same as scores below the mean
B) that extreme scores are possible in the tails of a normal distribution
C) that there are an infinite number of possible normal distributions
D) that this characteristic has no practical implication

Question 14

In a normal distribution,50% of all data:

A) fall above the mean.
B) fall below the median.
C) fall above and below the mode.
D) all of these.

Question 15

Scores far from the mean are located in the ______ of a normal distribution.

A) body
B) tails
C) most sensitive areas
D) most uncertain areas

Question 16

A professor finds that the students scored a 76 ± 8 (M ± SD)on the final exam.On this exam,a score of 90 is an A. Assuming these data are normally distributed, what is the z score for 90 (the cutoff for an A)?

A) 1.75
B) 1.50
C) 1.25
D) There is not enough information to answer this question.

Question 17

Which of the following is a possible value for the standard deviation of a normal distribution?

A) - $\infty$
B) 0
C) -2
D) 0.5

Question 18

The mean can take on any value and the standard deviation can take on any positive value.Therefore,

A) scores above the mean are distributed the same as scores below the mean.
B) extreme scores are possible in a normal distribution.
C) there are an infinite number of possible normal distributions.
D) this characteristic has no practical implication.

Question 19

A researcher finds that the average preschool-aged child drinks two cups of milk per day.Assuming these data are normally distributed,the z score for the average cups per day in this example is

A) less than 0.
B) greater than 0.
C) exactly equal to 0.
D) there is not enough information to answer this question.

Question 20

Most behavior is believed to ______ a normal distribution.

A) be exactly equal to
B) not resemble at all
C) approximate

Question 21

A researcher records the following body mass index (BMI)scores for a group of participants: 28.4 ± 1.6 (M ± SD).Participants who score between 25 and 30 on this scale are categorized as overweight.What percentage of participants fell in this overweight category?

A) .4834
B) .1753
C) .8413
D) .8247

Question 22

State whether the first area is bigger,the second area is bigger,or the two areas are equal: the area to the left of z = 1.00,or the area to the left of z = -1.00.

A) The first area is bigger.
B) The second area is bigger.
C) The two areas are the same.

Question 23

Which of the following is required to locate proportions of area under the normal curve?

A) compute a z-transformation
B) find the probability of a z score in the unit normal table
C) compute a z-transformation and find the probability of a z score in the unit normal table
D) none of these

Question 24

A researcher records the following time spent sleeping per night (in hours)in a group of participants: 5.8 ± 1.8 (M ± SD).The researcher decides to categorize participants who sleep between 6 and 8 hr as moderate sleepers.What percentage of participants fell in this category?

A) about 39%
B) about 11%
C) about 35%
D) about 7%

Question 25

A researcher records the following response times to a visual stimulus: 23 ± 3.1 (M ± SD)s.Assuming these data are normally distributed,what is the probability that participants responded in 20 s or less?

A) .1660
B) .3340
C) .6660
D) The probability is not listed in the unit normal table.

Question 26

Which of the following proportions is largest in a z distribution?

A) The proportion of area above the mean.
B) The proportion of area between z = +1 and z = -1.
C) The proportion of area greater than z = 1.0.
D) The proportion of area less than z = 0.

Question 27

Which of the following is not a step to locate a proportion in a normal distribution?

A) transform a raw score (x) into a z score
B) locate the corresponding proportion for the z score in the unit normal table
C) convert a proportion to a standard normal z score

Question 28

A counselor records the number of disagreements (per session)among couples during group counseling sessions.If the number of disagreements is distributed normally as 4.4 ± 0.4 (M ± SD)disagreements,then what proportion of couples disagree at least four times during each counseling session?

A) .3413
B) .1587
C) .8413
D) The probability is not listed in the unit normal table.

Question 29

Two normal distributions are observed.The first distribution has a mean of 12 and a standard deviation of 2.The second distribution has a mean of 0 and a standard deviation of 2.For which distribution will the z score for the mean be larger?

A) the first z distribution
B) the second distribution
C) none, the z score will be the same

Question 30

Which of the following is required to locate z scores with a given proportion?

A) find the z score associated with a given probability
B) compute a z transformation to find the raw score
C) find the z score associated with a given probability and compute a z transformation to find the raw score
D) none of these

Question 31

State whether the first area is bigger,the second area is bigger,or the two areas are equal: the area to the left of z = 0.80,or the area to the right of z = -0.80.

A) The first area is bigger.
B) The second area is bigger.
C) The two areas are the same.

Question 32

What is the z score for scores in the top and bottom 2.5%?

A) ±1.96
B) 1.96
C) .0124
D) ±.675

Question 33

A researcher records the following number of birdcalls made during an experimental session with robins: 7.2 ± 0.6 (M ± SD).Assuming these data are normally distributed,what is the probability that robins made more than nine birdcalls during this experimental session?

A) .9987
B) .4987
C) .0013
D) The probability is not listed in the unit normal table.

Question 34

A researcher records the following assessment data: 42 ± 6 (M ± SD).The researcher only wants to sample participants scoring in the top 20% of this assessment.What is the cutoff score for the top 20% in this example?

A) 0.84
B) 47.04
C) 36.96
D) There is not enough information to answer this question.

Question 35

A professor records the following final exam scores: 78 ± 7 (M ± SD).Students scoring in the top 14% get an A. What is the cutoff score for the top 14% in this example?

A) 1.08
B) 70.44
C) 85.56
D) There is not enough information to answer this question.

Question 36

A researcher measures the number of tasks completed by participants during a 5-min multitasking session.If the number of tasks completed is distributed normally as 6.3 ± 1.0 (M ± SD)tasks,then what is the probability that participants completed less than eight tasks?

A) .0446
B) .9554
C) .4554
D) The probability is not listed in the unit normal table.

Question 37

What is the z score for scores in the bottom 5%?

A) 1.645
B) -1.645
C) .4801
D) The score is not listed in the table.

Question 38

State whether the first area is bigger,the second area is bigger,or the two areas are equal: the area to the right of the mean,or the area between z = ±1.00.

A) The first area is bigger.
B) The second area is bigger.
C) The two areas are the same.

Question 39

A researcher records the following times (in seconds)that it took a group of mice to complete a maze: 23 ± 4.1 (M ± SD).The top 10% of mice finishing with the fastest times will be placed in a "maze bright" group.What is the cutoff time to be placed in this group?

A) 17.75 s
B) 28.25 s
C) faster than 16 s
D) There is not enough information to answer this question.

Question 40

What is the z score for scores in the bottom 10%?

A) 1.28
B) 2.32
C) -2.32
D) -1.28

Question 41

A standard normal distribution is a specific example of one of the infinitely possible normal distributions that could exist.

Question 42

An example of a binomial variable includes

A) time (in seconds).
B) weight (in pounds).
C) sex (male, female).
D) all of these.

Question 43

What is the z score for scores in the top 2.5%?

A) .675
B) 1.96
C) .0124
D) .0250

Question 44

The standard deviation and the mean can equal 0 in a data set that is normally distributed.

Question 45

The mean,median,and mode are all located at the 50th percentile in a standard normal distribution.

Question 46

The total area under a normal curve increases as the standard deviation increases.

Question 47

An assumption of normality is largely used for statistical inference and theory.

Question 48

In a hypothetical job field,10% of workers are promoted within their first year of employment.For this hypothetical job field,what is the probability that exactly 25 workers were promoted in their first year in a random sample of 200 workers? Hint: This is a binomial distribution,where p = .10 and q = .90.

A) less than 5%
B) greater than 95%
C) between 5% and 6%
D) between 15% and 16%

Question 49

The ______ are the range of continuous values containing the score of interest in a binomial distribution.

A) observed limits
B) approximate limits
C) real limits
D) speed limits

Question 50

A researcher wants to know the probability of being named on the honor roll from a population where 8% of students are on the honor roll.If the researcher selects a sample of 400 students,then what is the mean number of students expected to be on the honor roll? Hint: This is a binomial distribution,where p = 0.08 and q = 0.92.

A) 29
B) 32
C) 368
D) 200

Question 51

The asymptotic tails in a normal distribution represent the possibility of outliers in a data set.

Question 52

Which of the following is not a step to locate a score in a normal distribution?

A) locate a z score associated with a given proportion in the unit normal table
B) transform a z score into a raw score (x)
C) transform a raw score (x) into a z score

Question 53

A researcher records the following times (in seconds)that it took a group of students to complete an exam: 18 ± 2 (M ± SD)min.How long did it take 80% of students to complete the exam?

A) less than 16 min
B) 16.32 min
C) less than 18 min
D) 19.68 min

Question 54

The closer a z score is to 0,the smaller the area is under the normal curve toward the tails.

Question 55

Most behavioral phenomena are believed to approximate the normal distribution.

Question 56

In a normal distribution,the mean can only take on positive values.

Question 57

Another name for a binomial variable is a

A) random variable.
B) systematic variable.
C) participant variable.
D) dichotomous variable.

Question 58

Which of the following is an appropriate step for the normal approximation of the binomial distribution?

A) check for normality
B) find the real limits
C) find the proportion located within the real limits
D) all of these

Question 59

When a z score equals 0,this means that there is no variability.

Question 60

A researcher wants to know the probability of selecting a student athlete from a school population where 5% of students are athletes.If the researcher selects a sample of 120 students,is it appropriate to use the normal approximation of the binomial distribution to estimate this probability?

A) Yes, because the sample size is large.
B) Yes, because nq is greater than 10.
C) No, because np is greater than 10.
D) No, because np is less than 10.

Question 61

The first step to locating proportions in a normal distribution is to first look up probabilities in the unit normal table.

Question 62

All z scores above the mean are positive,whereas all z scores below the mean are negative.

Question 63

For a set of data with 25 ± 2.5,at least 95% of scores fall between 20 and 30.

Question 64

A z score for the mean in a normal distribution is always equal to 0.

Question 65

The unit normal table can be used to find the probability of a particular score in both normal and nonnormal distributions.

Question 66

For a set of data with 5 ± 1.5,at least 95% of scores are greater than 3.0.

Question 67

The unit normal table can be used to find the probability of a particular score for most,but certainly not all,possible normal distributions.

Question 68

In a normal distribution,the probability of a score above the mean is larger than the probability of a score between first standard deviation above and below the mean.

Question 69

It is appropriate to use the normal approximation of the binomial distribution with a sample of 100 participants,where p = .07 and q = .93.

Question 70

The z score cutoff for the top 50% of scores in any normal distribution is 0.

Question 71

The standard normal distribution can be used to estimate probabilities with known raw scores,but it cannot be used to estimate raw scores with known probabilities.

Question 72

The binomial probability distribution is distributed with and .

Question 73

In a normal distribution,the probability of a score above -1.0 SD is equal to the probability of a score below +1.0 SD.

Question 74

In a normal distribution with 2.2 ± 4.1 (M ± SD),a researcher can appropriately conclude that most scores occurred above the mean.

Question 75

A researcher selected data that were normally distributed and appropriately concluded that about 68.26% of scores occurred within one standard deviation of the mean.

Question 76

Data were normally distributed as 3.6 ± 0.6 (M ± SD).Hence,69.15% of data occurred below a score of 3.9 in this distribution.

Question 77

In a normal distribution with 3 ± 1 (M ± SD),a researcher can appropriately conclude that about 84.13% of scores were greater than 2.

Question 78

A binomial probability distribution is the distribution of random outcomes for a bivariate or dichotomous random variable.

Question 79

Data are normally distributed as 12.5 ± 0.5 (M ± SD).A score of 13.2 marks the top 30% of scores in this distribution.

Question 80

In a normal distribution,a score of 8 will always be more probable than a score of 0.