Ch. 5
What is the z score for scores in the top 2.5%?
+1.96
A researcher determines that students are active about 60 ± 12 (M ± SD) minutes per day. Assuming these data are normally distributed, what is the z score for students being active 48 min per week?
-1.0
A researcher determines that students study an average of 80 ± 20 (M ± SD) minutes per week. Assuming these data are normally distributed, what is the z score for students studying 60 min per week?
-1.0
What is the z score for scores in the bottom 10%?
-1.28
What is the z score for scores in the bottom 5%?
-1.645
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?
.0013
A researcher has participants choose between three advertisements. She finds that 54 prefer Ad A, 86 prefer Ad B, and 60 prefer Ad C. The probability or proportion of participants preferring Ad B is ______.
.43
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?
.8247
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 4 times during each counseling session?
.8413
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 8 tasks?
.9554
Which of the following is a possible value for the standard deviation of a normal distribution?
0.5
A therapist goes through her records and finds that 200 of her 400 patients showed significant improvement in mental health over the past year. Hence, the probability of her patients showing significant improvement in mental health is ______.
0.50
The standard normal distribution is normally distributed with a mean of ______ and a variance of ______.
0; 1
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)?
1.75
A news poll showed that voters had no preference for either of three candidates. In this example, the probability of a vote for, say, Candidate A equals ______.
1/3
A researcher records the following response times to a visual stimulus: 23 ± 3.1 (M ± SD) seconds. Assuming these data are normally distributed, what is the probability that participants responded in 20 s or less?
1660
A researcher records the following times (in seconds) that it took a group of students to complete an exam: 18 ± 2 min (M ± SD). How long did it take 80% of students to complete the exam?
19.68 min
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?
28.25 s
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?
47.04
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?
85.56
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?
No, because the z score for 5 bites is greater than 0.
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?
None, the z score will be the same.
Which of the following is NOT a characteristic of probability?
Probability is most useful for describing fixed events.
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.
The first area is bigger.
Which of the following describes the largest proportion in a z distribution?
The proportion of area between z = +1 and z = -1.
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.
The second area is bigger.
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.
The two areas are the same.
Which of the following is required to locate z scores with a given proportion?
both A and B (find the z score associated with a given probability, compute a z transformation to find the raw score)
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 two symptoms per day is 0. Assuming these data are normally distributed, did she reach her goal?
Yes, because a z score of 0 is the average, or mean.
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?
about 35%
In a normal distribution, 50% of all data ______.
all of these (fall above the mean, fall below the median, fall above and below the mode)
A theoretical distribution that evenly distributes data around the mean, median, and mode is called the ______.
all of these (normal distribution, bell-shaped distribution, Gaussian distribution)
By definition, the probability of an outcome or event is ______.
all of these (the proportion of times an outcome is likely to occur, the fraction of times an outcome is likely to occur, particularly useful for predicting the likelihood of random events)
Most behavior is believed to ______ a normal distribution.
approximate
Which of the following is required to locate proportions of area under the normal curve?
both A and B (compute a z-transformation, find the probability of a z score in the unit normal table.)
Which of the following is not a step to locate a proportion in a normal distribution?
convert a proportion to a standard normal z score
A researcher visits a population of 1,200 local residents to determine the proportion of local residents who support a new smoking ban. In this case, the sample space is ______.
equal to the population of 1,200 local residents
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 ______.
exactly equal to 0
The total number of possible outcomes for a random variable is referred to as ______.
the sample space
The following distribution most closely approximates a ______.
normal distribution
The proportion or fraction of times an outcome is likely to occur is referred to as ______.
probability
The normal distribution is symmetrical, which means that ______.
scores above the mean are distributed the same as scores below the mean
A distribution of z scores are distributed in what type of unit of measurement?
standard deviation units
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.
standard normal transformation
Scores far from the mean are located in the ______ of a normal distribution.
tails
What is the implication for the tails of a normal distribution being asymptotic?
that extreme scores are possible in the tails of a normal distribution
The normal distribution has all of the following characteristics, except that ______.
the total area under the curve is greater than 1.0
The mean can take on any value and the standard deviation can take on any positive value. Therefore, ______.
there are an infinite number of possible normal distributions
Which of the following is not a step to locate a score in a normal distribution?
transform a raw score (x) into a z score
The unit of measurement distributed along the x-axis of a standard normal distribution is referred to as a ______.
z score
What is the z score for scores in the top and bottom 2.5%?
±1.96
